Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-09T19:45:46.520Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  29 April 2019

Paul Romatschke
Affiliation:
University of Colorado Boulder
Ulrike Romatschke
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Relativistic Fluid Dynamics In and Out of Equilibrium
And Applications to Relativistic Nuclear Collisions
, pp. 172 - 193
Publisher: Cambridge University Press
Print publication year: 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Maxwell, J. C.. On the dynamical theory of gases. Phil. Trans. R. Soc., 157:49, 1867.Google Scholar
Cattaneo, C.. Sulla conduzione del calore. Atti Sem. Mat. Fis. Univ. Modena, 3:3, 1948.Google Scholar
Müller, I.. Zum Paradoxon der Warmeleitungstheorie. Z. Phys., 198:329344, 1967.CrossRefGoogle Scholar
Israel, W.. Nonstationary irreversible thermodynamics: A causal relativistic theory. Annals Phys., 100:310331, 1976.CrossRefGoogle Scholar
Israel, W. and Stewart, J. M.. Transient relativistic thermodynamics and kinetic theory. Annals Phys., 118:341372, 1979.CrossRefGoogle Scholar
Bjorken, J. D.. Highly relativistic nucleus–nucleus collisions: The central rapidity region. Phys. Rev., D27:140151, 1983.Google Scholar
Hosoya, A. and Kajantie, K.. Transport coefficients of QCD matter. Nucl. Phys., B250:666688, 1985.CrossRefGoogle Scholar
Baym, G., Monien, H., Pethick, C. J., and Ravenhall, D. G.. Transverse interactions and transport in relativistic quark–gluon and electromagnetic plasmas. Phys. Rev. Lett., 64:18671870, 1990.CrossRefGoogle ScholarPubMed
Heiselberg, H.. Viscosities of quark–gluon plasmas. Phys. Rev., D49:47394750, 1994, hep-ph/9401309.Google Scholar
Ollitrault, J.-Y.. Anisotropy as a signature of transverse collective flow. Phys. Rev., D46:229245, 1992.Google Scholar
Schnedermann, E., Sollfrank, J., and Heinz, U. W.. Thermal phenomenology of hadrons from 200-A/GeV S+S collisions. Phys. Rev., C48:24622475, 1993, nucl-th/9307020.Google Scholar
Kolb, P. F., Huovinen, P., Heinz, U. W., and Heiselberg, H.. Elliptic flow at SPS and RHIC: From kinetic transport to hydrodynamics. Phys. Lett., B500:232240, 2001, hep-ph/0012137.CrossRefGoogle Scholar
Teaney, D., Lauret, J., and Shuryak, E. V.. Flow at the SPS and RHIC as a quark gluon plasma signature. Phys. Rev. Lett., 86:47834786, 2001, nucl-th/0011058.CrossRefGoogle ScholarPubMed
Huovinen, P., Kolb, P. F., Heinz, U. W., Ruuskanen, P. V., and Voloshin, S. A.. Radial and elliptic flow at RHIC: Further predictions. Phys. Lett., B503:5864, 2001, hep-ph/0101136.CrossRefGoogle Scholar
Hirano, T. and Tsuda, K.. Collective flow and two pion correlations from a relativistic hydrodynamic model with early chemical freezeout. Phys. Rev., C66:054905, 2002, nucl-th/0205043.Google Scholar
Nonaka, C. and Bass, S. A.. Space-time evolution of bulk QCD matter. Phys. Rev., C75:014902, 2007, nucl-th/0607018.Google Scholar
Arnold, P. B., Moore, G. D., and Yaffe, L. G.. Transport coefficients in high temperature gauge theories. 1. Leading log results. JHEP, 11:001, 2000, hep-ph/0010177.CrossRefGoogle Scholar
Maldacena, J. M.. The L. N limit of superconformal field theories and super-gravity. Int. J. Theor. Phys., 38:11131133, 1999, hep-th/9711200. [Adv. Theor. Math. Phys.2,231(1998)].CrossRefGoogle Scholar
Policastro, G., Son, D. T., and Starinets, A. O.. The shear viscosity of strongly coupled N=4 supersymmetric Yang–Mills plasma. Phys. Rev. Lett., 87:081601, 2001, hep-th/0104066.CrossRefGoogle ScholarPubMed
Teaney, D.. The Effects of viscosity on spectra, elliptic flow, and HBT radii. Phys. Rev., C68:034913, 2003, nucl-th/0301099.Google Scholar
Muronga, A.. Second order dissipative fluid dynamics for ultrarelativistic nuclear collisions. Phys. Rev. Lett., 88:062302, 2002, nucl-th/0104064. [Erratum: Phys. Rev. Lett.89,159901(2002)].CrossRefGoogle ScholarPubMed
Muronga, A.. Causal theories of dissipative relativistic fluid dynamics for nuclear collisions. Phys. Rev., C69:034903, 2004, nucl-th/0309055.Google Scholar
Adcox, K. et al. Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration. Nucl. Phys., A757:184283, 2005, nucl-ex/0410003.CrossRefGoogle Scholar
Arsene, I. et al. Quark gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment. Nucl. Phys., A757:127, 2005, nuclex/0410020.CrossRefGoogle Scholar
Back, B. B. et al. The PHOBOS perspective on discoveries at RHIC. Nucl. Phys., A757:28101, 2005, nucl-ex/0410022.CrossRefGoogle Scholar
Adams, J. et al. Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration’s critical assessment of the evidence from RHIC collisions. Nucl. Phys., A757:102183, 2005, nuclex/0501009.CrossRefGoogle Scholar
Brookhaven National Laboratory. RHIC scientists serve up “perfect” liquid. https://tinyurl.com/ybb9scu2, 2005.Google Scholar
Baier, R., Romatschke, P., Son, D. T., Starinets, A. O., and Stephanov, M. A.. Relativistic viscous hydrodynamics, conformal invariance, and holography. JHEP, 04:100, 2008, 0712.2451.CrossRefGoogle Scholar
Bhattacharyya, S., Hubeny, V. E., Minwalla, S., and Rangamani, M.. Nonlinear fluid dynamics from gravity. JHEP, 02:045, 2008, 0712.2456.CrossRefGoogle Scholar
Romatschke, P. and Romatschke, U.. Viscosity information from relativistic nuclear collisions: How perfect is the fluid observed at RHIC? Phys. Rev. Lett., 99:172301, 2007, 0706.1522.CrossRefGoogle ScholarPubMed
Chaudhuri, A. K.. Saturation of elliptic flow and shear viscosity. 2007, 0708.1252.Google Scholar
Song, H. and Heinz, U. W.. Suppression of elliptic flow in a minimally viscous quark-gluon plasma. Phys. Lett., B658:279283, 2008, 0709.0742.CrossRefGoogle Scholar
Dusling, K. and Teaney, D.. Simulating elliptic flow with viscous hydrodynamics. Phys. Rev., C77:034905, 2008, 0710.5932.Google Scholar
Alver, B. and Roland, G.. Collision geometry fluctuations and triangular flow in heavy-ion collisions. Phys. Rev., C81:054905, 2010, 1003.0194. [Erratum: Phys. Rev. C82, 039903 (2010)].Google Scholar
Gubser, S. S.. Symmetry constraints on generalizations of Bjorken flow. Phys. Rev., D82:085027, 2010, 1006.0006.Google Scholar
Florkowski, W. and Ryblewski, R.. Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions. Phys. Rev., C83:034907, 2011, 1007.0130.Google Scholar
Martinez, Mauricio and Strickland, Michael. Dissipative dynamics of highly anisotropic systems. Nucl. Phys., A848:183197, 2010, 1007.0889.CrossRefGoogle Scholar
Schenke, B., Jeon, S., and Gale, C.. Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics. Phys. Rev. Lett., 106:042301, 2011, 1009.3244.CrossRefGoogle Scholar
Khachatryan, V. et al. Observation of long-range near-side angular correlations in proton-proton collisions at the LHC. JHEP, 09:091, 2010, 1009.4122.CrossRefGoogle Scholar
Chatrchyan, S. et al. Observation of long-range near-side angular correlations in proton-lead collisions at the LHC. Phys. Lett., B718:795814, 2013, 1210.5482.CrossRefGoogle Scholar
Abelev, B. et al. Long-range angular correlations on the near and away side in p-Pb collisions at Phys. Lett., B719:2941, 2013, 1212.2001.CrossRefGoogle Scholar
Aad, G. et al. Observation of associated near-side and away-side long-range correlations in proton-lead collisions with the ATLAS detector. Phys. Rev. Lett., 110(18):182302, 2013, 1212.5198.CrossRefGoogle ScholarPubMed
Chatrchyan, S. et al. Multiplicity and transverse momentum dependence of two-and four-particle correlations in pPb and PbPb collisions. Phys. Lett., B724: 213–240, 2013, 1305.0609.Google Scholar
Heller, M. P. and Spaliński, M.. Hydrodynamics beyond the gradient expansion: resurgence and resummation. Phys. Rev. Lett., 115(7):072501, 2015, 1503.07514.CrossRefGoogle ScholarPubMed
Adare, A. et al. Measurements of mass-dependent azimuthal anisotropy in central p+Au, d+Au, and 3He+Au collisions at Submitted to: Phys. Rev. C, 2017, 1710.09736.Google Scholar
Abbott, B. P. et al. Properties of the binary black hole merger GW150914. Phys. Rev. Lett., 116(24):241102, 2016, 1602.03840.CrossRefGoogle ScholarPubMed
Abbott, B. P. et al. Tests of general relativity with GW150914. Phys. Rev. Lett., 116(22):221101, 2016, 1602.03841.CrossRefGoogle ScholarPubMed
Salzer, J.. Light-like viscous fluids in near-horizon extremal Kerr backgrounds. Bachelor thesis, Technical University of Vienna, unpublished, 2012.Google Scholar
Berges, J., Rothkopf, A., and Schmidt, J.. Non-thermal fixed points: Effective weak-coupling for strongly correlated systems far from equilibrium. Phys. Rev. Lett., 101:041603, 2008, 0803.0131.CrossRefGoogle Scholar
Euler, L.. Principes généraux de l’état d’équilibre d’un fluide. Mem. Acad. Sci. Berlin, 11:217273, 1755.Google Scholar
Gubser, S. S. and Yarom, A.. Conformal hydrodynamics in Minkowski and de Sitter spacetimes. Nucl. Phys., B846:469511, 2011, 1012.1314.CrossRefGoogle Scholar
Tolman, R. C.. Static solutions of Einstein’s field equations for spheres of fluid. Phys. Rev., 55:364373, 1939.CrossRefGoogle Scholar
Oppenheimer, J. R. and Volkoff, G. M.. On Massive neutron cores. Phys. Rev., 55:374381, 1939.CrossRefGoogle Scholar
Romatschke, P.. Relativistic viscous fluid dynamics and non-equilibrium entropy. Class. Quant. Grav., 27:025006, 2010, 0906.4787.CrossRefGoogle Scholar
Attems, M., Bea, Y., Casalderrey-Solana, J., Mateos, D., Triana, M., and Zilhao, M.. Holographic Collisions across a Phase Transition. 2018, 1807.05175.CrossRefGoogle Scholar
El, A., Xu, Z., and Greiner, C.. Third-order relativistic dissipative hydrodynamics. Phys. Rev., C81:041901, 2010, 0907.4500.Google Scholar
Jaiswal, A.. Relativistic third-order dissipative fluid dynamics from kinetic theory. Phys. Rev., C88:021903, 2013, 1305.3480.Google Scholar
Chattopadhyay, C., Jaiswal, A., Pal, S., and Ryblewski, R.. Relativistic third-order viscous corrections to the entropy four-current from kinetic theory. Phys. Rev., C91(2):024917, 2015, 1411.2363.Google Scholar
Grozdanov, S. and Kaplis, N.. Constructing higher-order hydrodynamics: the third order. Phys. Rev., D93(6):066012, 2016, 1507.02461.Google Scholar
Hiscock, W. A. and Lindblom, L.. Generic instabilities in first-order dissipative relativistic fluid theories. Phys. Rev., D31:725733, 1985.Google Scholar
Landau, L. D. and Lifshitz, E. M.. Fluid mechanics. Elsevier, 2nd edition, 1987.Google Scholar
Navier, C. L. M. H.. Mémoire sur les lois du mouvement des fluides. Mém. Acad. Sci. Inst. France, 6:389440, 1822.Google Scholar
Stokes, G. G.. On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Trans. Camb. Philos. Soc., 8:287319, 1845.Google Scholar
Burnett, D.. The distribution of velocities and mean motion in a slight nonuniform gas. Proc. London Math. Soc., 39:385, 1935.CrossRefGoogle Scholar
Duff, M. J.. Twenty years of the Weyl anomaly. Class. Quant. Grav., 11:13871404, 1994, hep-th/9308075.CrossRefGoogle Scholar
Aharony, O., Gubser, S. S., Maldacena, J. M., Ooguri, H., and Oz, Y.. Large N field theories, string theory and gravity. Phys. Rept., 323:183386, 2000, hep-th/9905111.CrossRefGoogle Scholar
Lu, E. and Moore, G. D.. The Bulk Viscosity of a Pion Gas. Phys. Rev., C83:044901, 2011, 1102.0017.Google Scholar
Arnold, P. B., Dogan, C., and Moore, G. D.. The bulk viscosity of high-temperature QCD. Phys. Rev., D74:085021, 2006, hep-ph/0608012.Google Scholar
Brevik, I., Grøn, Ø., de Haro, J., Odintsov, S. D., and Saridakis, E. N.. Viscous cosmology for early- and late-time universe. Int. J. Mod. Phys., D26(14):1730024, 2017, 1706.02543.CrossRefGoogle Scholar
Rajagopal, K. and Tripuraneni, N.. Bulk viscosity and cavitation in boost-invariant hydrodynamic expansion. JHEP, 03:018, 2010, 0908.1785.CrossRefGoogle Scholar
Bhatt, J. R., Mishra, H., and Sreekanth, V.. Cavitation and thermal photon production in relativistic heavy ion collisions. 2010, 1005.2756.Google Scholar
Klimek, A., Leblond, L., and Sinha, A.. Cavitation in holographic sQGP. Phys. Lett., B701:144150, 2011, 1103.3987.CrossRefGoogle Scholar
Habich, M. and Romatschke, P.. Onset of cavitation in the quark-gluon plasma. JHEP, 12:054, 2014, 1405.1978.CrossRefGoogle Scholar
Sanches, S. M., Fogaça, D. A., Navarra, F. S., and Marrochio, H.. Cavitation in a quark gluon plasma with finite chemical potential and several transport coefficients. Phys. Rev., C92(2):025204, 2015, 1505.06335.Google Scholar
Zimdahl, W.. Bulk viscous cosmology. Phys. Rev., D53:54835493, 1996, astroph/9601189.Google Scholar
Gagnon, J.-S. and Lesgourgues, J.. Dark goo: Bulk viscosity as an alternative to dark energy. JCAP, 1109:026, 2011, 1107.1503.CrossRefGoogle Scholar
Janik, R. A. and Peschanski, R. B.. Asymptotic perfect fluid dynamics as a consequence of Ads/CFT. Phys. Rev., D73:045013, 2006, hep-th/0512162.Google Scholar
Bantilan, H., Ishii, T., and Romatschke, P.. Holographic heavy-ion collisions: Analytic solutions with longitudinal flow, elliptic flow and vorticity. 2018, 1803.10774.CrossRefGoogle Scholar
Belenkij, S. Z. and Landau, L. D.. Hydrodynamic theory of multiple production of particles. Nuovo Cim. Suppl., 3S10:15, 1956. [Usp. Fiz. Nauk56,309(1955)].CrossRefGoogle Scholar
Chesler, P. M. and Yaffe, L. G.. Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory. Phys. Rev., D82:026006, 2010, 0906.4426.Google Scholar
Heller, M. P., Janik, R. A., and Witaszczyk, P.. The characteristics of thermalization of boost-invariant plasma from holography. Phys. Rev. Lett., 108:201602, 2012, 1103.3452.CrossRefGoogle ScholarPubMed
Wu, B. and Romatschke, P.. Shock wave collisions in AdS5: approximate numerical solutions. Int. J. Mod. Phys., C22:13171342, 2011, 1108.3715.CrossRefGoogle Scholar
van der Schee, Wilke. Holographic thermalization with radial flow. Phys. Rev., D87(6):061901, 2013, 1211.2218.Google Scholar
Casalderrey-Solana, J., Heller, M. P., Mateos, D., and van der Schee, W.. From full stopping to transparency in a holographic model of heavy ion collisions. Phys. Rev. Lett., 111:181601, 2013, 1305.4919.CrossRefGoogle Scholar
Kurkela, A. and Zhu, Y.. Isotropization and hydrodynamization in weakly coupled heavy-ion collisions. Phys. Rev. Lett., 115(18):182301, 2015, 1506.06647.CrossRefGoogle ScholarPubMed
Keegan, L., Kurkela, A., Romatschke, P., van der Schee, W., and Zhu, Y.. Weak and strong coupling equilibration in nonabelian gauge theories. JHEP, 04:031, 2016, 1512.05347.Google Scholar
Attems, M., Bea, Y., Casalderrey-Solana, J., Mateos, D., Triana, M., and Zilhao, M.. Phase transitions, inhomogeneous horizons and second-order hydrodynamics. 2017, 1703.02948.CrossRefGoogle Scholar
Heller, M. P., Janik, R. A., and Witaszczyk, P.. Hydrodynamic gradient expansion in gauge theory plasmas. Phys. Rev. Lett., 110(21):211602, 2013, 1302.0697.CrossRefGoogle ScholarPubMed
Buchel, A., Heller, M. P., and Noronha, J.. entropy production, hydrodynamics, and resurgence in the primordial quark-gluon plasma from holography. Phys. Rev., D94(10):106011, 2016, 1603.05344.Google Scholar
Denicol, G. S. and Noronha, J.. Divergence of the Chapman-Enskog expansion in relativistic kinetic theory. 2016, 1608.07869.Google Scholar
Heller, M. P., Kurkela, A., and Spaliński, M.. Hydrodynamization and transient modes of expanding plasma in kinetic theory. 2016, 1609.04803.Google Scholar
Casalderrey-Solana, J., Gushterov, N. I., and Meiring, B.. Resurgence and hydrodynamic attractors in Gauss-Bonnet holography. 2017, 1712.02772.CrossRefGoogle Scholar
Santos, A., Brey, J. J., and Dufty, J. W.. Divergence of the Chapman-Enskog expansion. Phys. Rev. Lett., 56:15711574, Apr 1986.CrossRefGoogle ScholarPubMed
Aniceto, I. and Spaliński, M.. Resurgence in extended hydrodynamics. Phys. Rev., D93(8):085008, 2016, 1511.06358.Google Scholar
Florkowski, W., Ryblewski, R., and Spaliński, M.. Gradient expansion for anisotropic hydrodynamics. Phys. Rev., D94(11):114025, 2016, 1608.07558.Google Scholar
Lublinsky, M. and Shuryak, E.. How much entropy is produced in strongly coupled Quark-Gluon Plasma (sQGP) by dissipative effects? Phys. Rev., C76:021901, 2007, 0704.1647.Google Scholar
Bu, Y. and Lublinsky, M.. Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics. JHEP, 11:064, 2014, 1409.3095.CrossRefGoogle Scholar
Romatschke, P.. Do nuclear collisions create a locally equilibrated quark-gluon plasma? Eur. Phys. J., C77(1):21, 2017, 1609.02820.CrossRefGoogle Scholar
Bhatt, J. R., Mishra, H., and Sreekanth, V.. Shear viscosity, cavitation and hydrodynamics at LHC. Phys. Lett., B704:486489, 2011, 1103.4333.CrossRefGoogle Scholar
Fogaça, D. A., Sanches, S. M., Fariello, R., and Navarra, F. S.. Bubble dynamics and the quark-hadron phase transition in nuclear collisions. Phys. Rev., C93(5):055204, 2016, 1601.04596.Google Scholar
Romatschke, P.. Far from equilibrium fluid dynamics. 2017, 1704.08699.Google Scholar
Denicol, G. S. and Noronha, J.. Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics. 2017, 1711.01657.CrossRefGoogle Scholar
Romatschke, P.. Relativistic hydrodynamic attractors with broken symmetries: Non-conformal and non-homogeneous. 2017, 1710.03234.CrossRefGoogle Scholar
Spaliński, M.. On the hydrodynamic attractor of Yang-Mills plasma. 2017, 1708.01921.Google Scholar
Florkowski, W., Maksymiuk, E., and Ryblewski, R.. Coupled kinetic equations for quarks and gluons in the relaxation time approximation. 2017, 1710.07095.CrossRefGoogle Scholar
Strickland, M., Noronha, J., and Denicol, G.. The anisotropic non-equilibrium hydrodynamic attractor. 2017, 1709.06644.Google Scholar
Behtash, A., Cruz-Camacho, C. N., and Martinez, M.. Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow. 2017, 1711.01745.CrossRefGoogle Scholar
Blaizot, J.-P. and Yan, L.. Fluid dynamics of out of equilibrium boost invariant plasmas. 2017, 1712.03856.Google Scholar
Blaizot, J. P., Iancu, E., and Rebhan, A.. On the apparent convergence of perturbative QCD at high temperature. Phys. Rev., D68:025011, 2003, hep-ph/0303045.Google Scholar
Casalderrey-Solana, J., Liu, H., Mateos, D., Rajagopal, K., and Wiedemann, U. A.. Gauge/string duality, hot QCD and heavy ion collisions. 2011, 1101.0618.Google Scholar
Romatschke, P.. New developments in relativistic viscous hydrodynamics. Int. J. Mod. Phys., E19:153, 2010, 0902.3663.CrossRefGoogle Scholar
Kovtun, P.. Lectures on hydrodynamic fluctuations in relativistic theories. J. Phys., A45:473001, 2012, 1205.5040.Google Scholar
Hiscock, W. A. and Lindblom, L.. Stability and causality in dissipative relativistic fluids. Annals Phys., 151:466496, 1983.CrossRefGoogle Scholar
Kostadt, P. and Liu, M.. Causality and stability of the relativistic diffusion equation. Phys. Rev., D62:023003, 2000.Google Scholar
Grimsditch, M., Bhadra, R., and Torell, L. M.. Shear waves through the glass-liquid transformation. Phys. Rev. Lett., 62:26162619, May 1989.CrossRefGoogle ScholarPubMed
Scarponi, F., Comez, L., Fioretto, D., and Palmieri, L.. Brillouin light scattering from transverse and longitudinal acoustic waves in glycerol. Phys. Rev. B, 70:054203, Aug 2004.CrossRefGoogle Scholar
Pontecorvo, E., Krisch, M., Cunsolo, A., Monaco, G., Mermet, A., Verbeni, R., Sette, F., and Ruocco, G.. High-frequency longitudinal and transverse dynamics in water. Phys. Rev. E, 71:011501, Jan 2005.CrossRefGoogle ScholarPubMed
Baggioli, M. and Trachenko, K.. Solidity of liquids: How holography knows it. 2018, 1807.10530.Google Scholar
Trachenko, K. and Brazhkin, V. V.. Collective modes and thermodynamics of the liquid state. Reports on Progress in Physics, 79(1):016502, 2016.CrossRefGoogle ScholarPubMed
Starinets, A. O.. Quasinormal modes of near extremal black branes. Phys. Rev., D66:124013, 2002, hep-th/0207133.Google Scholar
Brewer, J. and Romatschke, P.. Nonhydrodynamic transport in trapped unitary fermi gases. Phys. Rev. Lett., 115(19):190404, 2015, 1508.01199.CrossRefGoogle ScholarPubMed
Bantilan, H., Brewer, J. T., Ishii, T., Lewis, W. E., and Romatschke, P.. String-theory-based predictions for nonhydrodynamic collective modes in strongly interacting Fermi gases. Phys. Rev., A94(3):033621, 2016, 1605.00014.CrossRefGoogle Scholar
Romatschke, P.. Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions. Eur. Phys. J., C76(6):352, 2016, 1512.02641.CrossRefGoogle Scholar
Grozdanov, S., Kaplis, N., and Starinets, A. O.. From strong to weak coupling in holographic models of thermalization. JHEP, 07:151, 2016, 1605.02173.CrossRefGoogle Scholar
Heller, M. P., Janik, R. A., Spaliński, M., and Witaszczyk, P.. Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma. Phys. Rev. Lett., 113(26):261601, 2014, 1409.5087.CrossRefGoogle ScholarPubMed
Romatschke, P.. Relativistic (Lattice) Boltzmann equation with non-ideal equation of state. Phys. Rev., D85:065012, 2012, 1108.5561.Google Scholar
Jaiswal, A., Ryblewski, R., and Strickland, M.. Transport coefficients for bulk viscous evolution in the relaxation time approximation. Phys. Rev., C90(4):044908, 2014, 1407.7231.Google Scholar
Arnold, P. B., Moore, G. D., and Yaffe, L. G.. Transport coefficients in high temperature gauge theories. 2. Beyond leading log. JHEP, 05:051, 2003, hep-ph/0302165.CrossRefGoogle Scholar
York, M. A. and Moore, G. D.. Second order hydrodynamic coefficients from kinetic theory. Phys. Rev., D79:054011, 2009, 0811.0729.Google Scholar
Romatschke, P. and Son, D. T.. Spectral sum rules for the quark-gluon plasma. Phys. Rev., D80:065021, 2009, 0903.3946.Google Scholar
Borsanyi, S., Fodor, Z., Hoelbling, C., Katz, S. D., Krieg, S., and Szabo, K. K.. Full result for the QCD equation of state with 2+1 flavors. Phys. Lett., B730:99104, 2014, 1309.5258.CrossRefGoogle Scholar
Bazavov, A. et al. Equation of state in (2+1)-flavor QCD. Phys. Rev., D90:094503, 2014, 1407.6387.Google Scholar
Nakamura, A. and Sakai, S.. Transport coefficients of gluon plasma. Phys. Rev. Lett., 94:072305, 2005, hep-lat/0406009.CrossRefGoogle ScholarPubMed
Meyer, H. B.. A Calculation of the shear viscosity in SU(3) gluodynamics. Phys. Rev., D76:101701, 2007, 0704.1801.Google Scholar
Haack, M. and Yarom, A.. Universality of second order transport coefficients from the gauge-string duality. Nucl. Phys., B813:140155, 2009, 0811.1794.CrossRefGoogle Scholar
Arnold, P., Vaman, D., Wu, C., and Xiao, W.. Second order hydrodynamic coefficients from 3-point stress tensor correlators via AdS/CFT. JHEP, 10:033, 2011, 1105.4645.Google Scholar
Moore, G. D. and Sohrabi, K. A.. Thermodynamical second-order hydrodynamic coefficients. JHEP, 11:148, 2012, 1210.3340.CrossRefGoogle Scholar
Meyer, H. B.. Transport properties of the quark-gluon plasma: A lattice QCD perspective. Eur. Phys. J., A47:86, 2011, 1104.3708.CrossRefGoogle Scholar
Philipsen, O. and Schäfer, C.. The second order hydrodynamic transport coefficient κ for the gluon plasma from the lattice. JHEP, 02:003, 2014, 1311.6618.CrossRefGoogle Scholar
Pasztor, A., Fodor, Z., Giordano, M., Katz, S. D., Pasztor, A., Ratti, C., Schaefer, A., Szabo, K. K., and Toth, B. C.. High statistics lattice study of stress tensor correlators in pure SU(3) gauge theory. 2018, 1802.07718.Google Scholar
Buchel, A.. Resolving disagreement for eta/s in a CFT plasma at finite coupling. Nucl. Phys., B803:166170, 2008, 0805.2683.CrossRefGoogle Scholar
Buchel, A. and Paulos, M.. Relaxation time of a CFT plasma at finite coupling. Nucl. Phys., B805:5971, 2008, 0806.0788.CrossRefGoogle Scholar
Buchel, A. and Paulos, M.. Second order hydrodynamics of a CFT plasma from boost invariant expansion. Nucl. Phys., B810:4065, 2009, 0808.1601.CrossRefGoogle Scholar
Saremi, O. and Sohrabi, K. A.. Causal three-point functions and nonlinear second-order hydrodynamic coefficients in AdS/CFT. JHEP, 11:147, 2011, 1105.4870.CrossRefGoogle Scholar
Grozdanov, S. and Starinets, A. O.. On the universal identity in second order hydrodynamics. JHEP, 03:007, 2015, 1412.5685.CrossRefGoogle Scholar
Grozdanov, S. and Starinets, A. O.. Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid. JHEP, 03:166, 2017, 1611.07053.CrossRefGoogle Scholar
Ding, H.-T., Karsch, F., and Mukherjee, S.. Thermodynamics of strong-interaction matter from Lattice QCD. Int. J. Mod. Phys., E24(10):1530007, 2015, 1504.05274.CrossRefGoogle Scholar
Buchel, A.. Bulk viscosity of gauge theory plasma at strong coupling. Phys. Lett., B663:286289, 2008, 0708.3459.CrossRefGoogle Scholar
Kanitscheider, I. and Skenderis, K.. Universal hydrodynamics of non-conformal branes. JHEP, 04:062, 2009, 0901.1487.CrossRefGoogle Scholar
Denicol, G. S., Niemi, H., Molnar, E., and Rischke, D. H.. Derivation of transient relativistic fluid dynamics from the Boltzmann equation. Phys. Rev., D85:114047, 2012, 1202.4551. [Erratum: Phys. Rev.D91,no.3,039902(2015)].Google Scholar
Banerjee, N., Bhattacharya, J., Bhattacharyya, S., Jain, S., Minwalla, S., and Sharma, T.. Constraints on fluid dynamics from equilibrium partition functions. JHEP, 09:046, 2012, 1203.3544.CrossRefGoogle Scholar
Bigazzi, F. and Cotrone, A. L.. An elementary stringy estimate of transport coefficients of large temperature QCD. JHEP, 08:128, 2010, 1006.4634.CrossRefGoogle Scholar
Finazzo, S. I., Rougemont, R., Marrochio, H., and Noronha, J.. Hydrodynamic transport coefficients for the non-conformal quark-gluon plasma from holography. JHEP, 02:051, 2015, 1412.2968.Google Scholar
Wu, C., Chen, Y., and Huang, M.. Fluid/gravity correspondence: Second order transport coefficients in compactified D4-branes. JHEP, 01:118, 2017, 1604.07765.CrossRefGoogle Scholar
Horsley, R. and Schoenmaker, W.. Quantum field theories out of thermal equilibrium. 1. General considerations. Nucl. Phys., B280:716734, 1987.CrossRefGoogle Scholar
Kleinert, P. and Probst, J.. Second-order hydrodynamics and universality in non-conformal holographic fluids. JHEP, 12:091, 2016, 1610.01081.CrossRefGoogle Scholar
Pomeau, Y. and Résibois, P.. Time dependent correlation functions and mode-mode coupling theories. Physics Reports, 19(2):63 – 139, 1975.CrossRefGoogle Scholar
Lifshitz, E. M. and Pitaevskii, L. P.. Statistical Physics, Part 2. Pergamon, 1980.Google Scholar
Kovtun, P., Moore, G. D., and Romatschke, P.. Towards an effective action for relativistic dissipative hydrodynamics. JHEP, 07:123, 2014, 1405.3967.CrossRefGoogle Scholar
Kovtun, P., Moore, G. D., and Romatschke, P.. The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics. Phys. Rev., D84:025006, 2011, 1104.1586.Google Scholar
Arnold, P. B.. Symmetric path integrals for stochastic equations with multiplicative noise. Phys. Rev., E61:60996102, 2000, hep-ph/9912209.CrossRefGoogle Scholar
Chou, K.-C., Su, Z.-B., Hao, B.-L., and Yu, L.. Equilibrium and nonequilibrium formalisms made unified. Phys. Rept., 118:1, 1985.CrossRefGoogle Scholar
Wang, E. and Heinz, U. W.. A Generalized fluctuation dissipation theorem for nonlinear response functions. Phys. Rev., D66:025008, 2002, hep-th/9809016.Google Scholar
Grozdanov, S. and Polonyi, J.. Viscosity and dissipative hydrodynamics from effective field theory. Phys. Rev., D91(10):105031, 2015, 1305.3670.Google Scholar
Harder, M., Kovtun, P., and Ritz, A.. On thermal fluctuations and the generating functional in relativistic hydrodynamics. JHEP, 07:025, 2015, 1502.03076.CrossRefGoogle Scholar
Crossley, M., Glorioso, P., and Liu, H.. Effective field theory of dissipative fluids. 2015, 1511.03646.Google Scholar
Haehl, F. M., Loganayagam, R., and Rangamani, M.. Two roads to hydrodynamic effective actions: a comparison. 2017, 1701.07896.Google Scholar
Peralta-Ramos, J. and Calzetta, E.. Shear viscosity from thermal fluctuations in relativistic conformal fluid dynamics. JHEP, 02:085, 2012, 1109.3833.CrossRefGoogle Scholar
Nahrgang, M., Herold, C., Leupold, S., Mishustin, I., and Bleicher, M.. The impact of dissipation and noise on fluctuations in chiral fluid dynamics. J. Phys., G40:055108, 2013, 1105.1962.CrossRefGoogle Scholar
Chafin, C. and Schäfer, T.. Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity. Phys. Rev., A87(2):023629, 2013, 1209.1006.CrossRefGoogle Scholar
Romatschke, P. and Young, R. E.. Implications of hydrodynamic fluctuations for the minimum shear viscosity of the dilute Fermi gas at unitarity. Phys. Rev., A87(5):053606, 2013, 1209.1604.CrossRefGoogle Scholar
Murase, K. and Hirano, T.. Relativistic fluctuating hydrodynamics with memory functions and colored noises. 2013, 1304.3243.Google Scholar
Young, C., Kapusta, J. I., Gale, C., Jeon, S., and Schenke, B.. Thermally Fluctuating Second-Order Viscous Hydrodynamics and Heavy-Ion Collisions. Phys. Rev., C91(4):044901, 2015, 1407.1077.Google Scholar
Kovtun, P.. Fluctuation bounds on charge and heat diffusion. J. Phys., A48(26):265002, 2015, 1407.0690.Google Scholar
Akamatsu, Y., Mazeliauskas, A., and Teaney, D.. A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion. Phys. Rev., C95(1):014909, 2017, 1606.07742.Google Scholar
Akamatsu, Y., Mazeliauskas, A., and Teaney, D.. Bulk viscosity from hydrodynamic fluctuations with relativistic hydro-kinetic theory. 2017, 1708.05657.CrossRefGoogle Scholar
Martinez, M. and Schaefer, T.. Hydrodynamic tails and a fluctuation bound on the bulk viscosity. 2017, 1708.01548.CrossRefGoogle Scholar
De Groot, S. R.. Relativistic Kinetic Theory. Principles and Applications. North-holland Pub. Co, 1980.Google Scholar
Laine, M. and Vuorinen, A.. Basics of thermal field theory. Lect. Notes Phys., 925:pp.1281, 2016, 1701.01554.CrossRefGoogle Scholar
Montvay, I. and Münster, G.. Quantum fields on a lattice. Cambridge monographs on mathematical physics. Cambridge Univ. Press, Cambridge, 1994.CrossRefGoogle Scholar
Boltzmann, L.. Vorlesungen über Gastheorie. Johann Ambrosius Barth Verlag, 1896.Google Scholar
Bhatnagar, P. L., Gross, E. P., and Krook, M.. A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems. Phys. Rev., 94:511525, May 1954.CrossRefGoogle Scholar
Romatschke, P.. Collective flow without hydrodynamics: simulation results for relativistic ion collisions. Eur. Phys. J., C75(9):429, 2015, 1504.02529.CrossRefGoogle Scholar
Romatschke, P. and Strickland, M.. Collective modes of an anisotropic quark gluon plasma. Phys. Rev., D68:036004, 2003, hep-ph/0304092.Google Scholar
Borghini, N. and Gombeaud, C.. Anisotropic flow far from equilibrium. Eur. Phys. J., C71:1612, 2011, 1012.0899.CrossRefGoogle Scholar
Romatschke, P.. Azimuthal anisotropies at high momentum from purely nonhydrodynamic transport. 2018, 1802.06804.CrossRefGoogle Scholar
Chapman, S. and Cowling, T. G.. The Mathematical Theory of Non-Uniform Gases, 3rd edition. Cambridge Univ. Press, Cambridge, 1990.Google Scholar
Dusling, K., Moore, G. D., and Teaney, D.. Radiative energy loss and v(2) spectra for viscous hydrodynamics. Phys. Rev., C81:034907, 2010, 0909.0754.Google Scholar
Strickland, M.. Anisotropic hydrodynamics: three lectures. Acta Phys. Polon., B45(12):23552394, 2014, 1410.5786.CrossRefGoogle Scholar
Nopoush, M., Strickland, M., Ryblewski, R., Bazow, D., Heinz, U., and Martinez, M.. Leading-order anisotropic hydrodynamics for central collisions. Phys. Rev., C92(4):044912, 2015, 1506.05278.Google Scholar
Alqahtani, M., Nopoush, M., and Strickland, M.. Relativistic anisotropic hydrodynamics. 2017, 1712.03282.CrossRefGoogle Scholar
Florkowski, W., Heller, M. P., and Spalinski, M.. New theories of relativistic hydrodynamics in the LHC era. 2017, 1707.02282.Google Scholar
Kurkela, A. and Wiedemann, U. A.. Analytic structure of nonhydrodynamic modes in kinetic theory. 2017, 1712.04376.Google Scholar
Teaney, D.. Finite temperature spectral densities of momentum and R-charge correlators in N=4 Yang Mills theory. Phys. Rev., D74:045025, 2006, hep-ph/0602044.Google Scholar
Blaizot, J.-P. and Iancu, E.. The Quark gluon plasma: Collective dynamics and hard thermal loops. Phys. Rept., 359:355528, 2002, hep-ph/0101103.CrossRefGoogle Scholar
Zaffaroni, A.. Introduction to the AdS-CFT correspondence. Class. Quant. Grav., 17:35713597, 2000.CrossRefGoogle Scholar
Policastro, G., Son, D. T., and Starinets, A. O.. From AdS / CFT correspondence to hydrodynamics. 2. Sound waves. JHEP, 12:054, 2002, hep-th/0210220.CrossRefGoogle Scholar
Kovtun, P. K. and Starinets, A. O.. Quasinormal modes and holography. Phys. Rev., D72:086009, 2005, hep-th/0506184.Google Scholar
Berti, E., Cardoso, V., and Starinets, A. O.. Quasinormal modes of black holes and black branes. Class. Quant. Grav., 26:163001, 2009, 0905.2975.CrossRefGoogle Scholar
Kovtun, P., Son, D. T., and Starinets, A. O.. Viscosity in strongly interacting quantum field theories from black hole physics. Phys. Rev. Lett., 94:111601, 2005, hep-th/0405231.CrossRefGoogle ScholarPubMed
Danielewicz, P. and Gyulassy, M.. Dissipative phenomena in quark gluon plasmas. Phys. Rev., D31:5362, 1985.Google Scholar
Kats, Y. and Petrov, P.. Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory. JHEP, 01:044, 2009, 0712.0743.CrossRefGoogle Scholar
Brigante, M., Liu, H., Myers, R. C., Shenker, S., and Yaida, S.. The viscosity bound and causality violation. Phys. Rev. Lett., 100:191601, 2008, 0802.3318.CrossRefGoogle ScholarPubMed
Spaliński, M.. Small systems and regulator dependence in relativistic hydrodynamics. Phys. Rev., D94(8):085002, 2016, 1607.06381.Google Scholar
de Haro, S., Solodukhin, S. N., and Skenderis, K.. Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence. Commun. Math. Phys., 217:595622, 2001, hep-th/0002230.CrossRefGoogle Scholar
Fefferman, C. and Graham, C.R.. Conformal invariants. Elie Cartan et les Mathématiques d’aujourd’hui, Astérisque, page 95, 1985.Google Scholar
Habich, M.. Cavitation in Heavy Ion Collisions. Bachelor thesis, unpublished, 2011.Google Scholar
Aarts, G. and Martinez Resco, J. M.. Transport coefficients, spectral functions and the lattice. JHEP, 04:053, 2002, hep-ph/0203177.CrossRefGoogle Scholar
Karsch, F.. Lattice QCD at high temperature and density. Lect. Notes Phys., 583:209249, 2002, hep-lat/0106019.CrossRefGoogle Scholar
Kapusta, J. I. and Charles Gale, . Finite-temperature field theory: Principles and applications. Cambridge University Press, 2011.Google Scholar
Luscher, M.. Trivializing maps, the Wilson flow and the HMC algorithm. Commun. Math. Phys., 293:899919, 2010, 0907.5491.CrossRefGoogle Scholar
Makino, H. and Suzuki, H.. Lattice energy–momentum tensor from the Yang–Mills gradient flow—inclusion of fermion fields. PTEP, 2014:063B02, 2014, 1403.4772. [Erratum: PTEP2015, 079202 (2015)].Google Scholar
Sommer, R.. Scale setting in lattice QCD. PoS, LATTICE2013:015, 2014, 1401.3270.Google Scholar
Morningstar, C. J. and Peardon, M. J.. The Glueball spectrum from an anisotropic lattice study. Phys. Rev., D60:034509, 1999, hep-lat/9901004.Google Scholar
Bornyakov, V. G. et al. Wilson flow and scale setting from lattice QCD. 2015, 1508.05916.Google Scholar
Hanada, M. and Romatschke, P.. Lattice simulations of 10d Yang-Mills toroidally compactified to 1d, 2d and 4d. Phys. Rev., D96(9):094502, 2017, 1612.06395.Google Scholar
Gottlieb, S. A., Liu, W., Toussaint, D., Renken, R. L., and Sugar, R. L.. Hybrid molecular dynamics algorithms for the numerical simulation of quantum chromodynamics. Phys. Rev., D35:25312542, 1987.Google Scholar
Bodeker, D., Moore, G. D., and Rummukainen, K.. Chern-Simons number diffusion and hard thermal loops on the lattice. Phys. Rev., D61:056003, 2000, hep-ph/9907545.Google Scholar
Rebhan, A., Romatschke, P., and Strickland, M.. Hard-loop dynamics of non-Abelian plasma instabilities. Phys. Rev. Lett., 94:102303, 2005, hep-ph/0412016.CrossRefGoogle ScholarPubMed
Berges, J., Gelfand, D., Scheffler, S., and Sexty, D.. Simulating plasma instabilities in SU(3) gauge theory. Phys. Lett., B677:210213, 2009, 0812.3859.CrossRefGoogle Scholar
Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D.. Hybrid Monte Carlo. Phys. Lett., B195:216222, 1987.CrossRefGoogle Scholar
DeGrand, T. and Detar, C. E.. Lattice methods for quantum chromodynamics. World Scientific, 2006.CrossRefGoogle Scholar
Borsanyi, S., Endrodi, G., Fodor, Z., Jakovac, A., Katz, S. D., Krieg, S., Ratti, C., and Szabo, K. K.. The QCD equation of state with dynamical quarks. JHEP, 11:077, 2010, 1007.2580.CrossRefGoogle Scholar
Patrignani, C. et al. Review of particle physics. Chin. Phys., C40(10):100001, 2016.Google Scholar
Aoki, Y., Borsanyi, S., Durr, S., Fodor, Z., Katz, S. D., Krieg, S., and Szabo, K. K.. The QCD transition temperature: results with physical masses in the continuum limit II. JHEP, 06:088, 2009, 0903.4155.CrossRefGoogle Scholar
Karsch, F., Redlich, K., and Tawfik, A.. Hadron resonance mass spectrum and lattice QCD thermodynamics. Eur. Phys. J., C29:549556, 2003, hep-ph/0303108.CrossRefGoogle Scholar
Borsanyi, S., Fodor, Z., Katz, S. D., Krieg, S., Ratti, C., and Szabo, K.. Fluctuations of conserved charges at finite temperature from lattice QCD. JHEP, 01:138, 2012, 1112.4416.CrossRefGoogle Scholar
Bazavov, A. et al. Fluctuations and correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model. Phys. Rev., D86:034509, 2012, 1203.0784.Google Scholar
Langelage, J. and Philipsen, O.. The pressure of strong coupling lattice QCD with heavy quarks, the hadron resonance gas model and the large N limit. JHEP, 04:055, 2010, 1002.1507.CrossRefGoogle Scholar
Blaizot, J. P., Iancu, E., and Rebhan, A.. Approximately selfconsistent resumma-tions for the thermodynamics of the quark gluon plasma. 1. Entropy and density. Phys. Rev., D63:065003, 2001, hep-ph/0005003.Google Scholar
Vuorinen, A.. The Pressure of QCD at finite temperatures and chemical potentials. Phys. Rev., D68:054017, 2003, hep-ph/0305183.Google Scholar
Laine, M. and Schroder, Y.. Quark mass thresholds in QCD thermodynamics. Phys. Rev., D73:085009, 2006, hep-ph/0603048.Google Scholar
Haque, N., Andersen, J. O., Mustafa, M. G., Strickland, M., and Su, N.. Three-loop pressure and susceptibility at finite temperature and density from hard-thermal-loop perturbation theory. Phys. Rev., D89(6):061701, 2014, 1309.3968.Google Scholar
MUSIC. 3+1d relativistic viscous hydrodynamics for heavy ion collisions. https://sourceforge.net/projects/music-hydro/, 2017.Google Scholar
superSONIC. A super-hybrid model for simulating relativistic ion collisions. https://sites.google.com/site/revihy/, version 2.1, 2016.Google Scholar
iEBE VISHNU. A convenient code package to automate event-by-event hydro + hadron cascade hybrid calculations in relativistic heavy-ion collisions. https://u.osu.edu/vishnu/, 2015.Google Scholar
Woods, R. D. and Saxon, D. S.. Diffuse surface optical model for nucleon-nuclei scattering. Phys. Rev., 95:577578, Jul 1954.CrossRefGoogle Scholar
De Jager, C. W., De Vries, H., and De Vries, C.. Nuclear charge- and magnetization-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables, 14(5–6):479 – 508, 1974. Nuclear Charge and Moment Distributions.CrossRefGoogle Scholar
De Vries, H., De Jager, C. W., and De Vries, C.. Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables, 36(3):495 – 536, 1987.CrossRefGoogle Scholar
Hulthén, L. and Sagawara, M.. Two nucleon interaction problem. Structure of Atomic Nuclei, Handbuch der Physik, 39:14, 1957.Google Scholar
Miller, M. L., Reygers, K., Sanders, S. J., and Steinberg, P.. Glauber modeling in high energy nuclear collisions. Ann. Rev. Nucl. Part. Sci., 57:205243, 2007, nucl-ex/0701025.CrossRefGoogle Scholar
Carlson, J. and Schiavilla, R.. Structure and dynamics of few nucleon systems. Rev. Mod. Phys., 70:743842, 1998.CrossRefGoogle Scholar
Nagle, J. L., Adare, A., Beckman, S., Koblesky, T., Orjuela Koop, J., McGlinchey, D., Romatschke, P., Carlson, J., Lynn, J. E., and McCumber, M.. Exploiting intrinsic triangular geometry in relativistic He3 +Au collisions to disentangle medium properties. Phys. Rev. Lett., 113(11):112301, 2014, 1312.4565.CrossRefGoogle Scholar
Venkat, S., Arrington, J., Miller, G. A., and Zhan, X.. Realistic transverse images of the proton charge and magnetic densities. Phys. Rev., C83:015203, 2011, 1010.3629.Google Scholar
Heinz, U. and Scott Moreland, J.. Energy dependent growth of the nucleon and hydrodynamic initial conditions. Phys. Rev., C84:054905, 2011, 1108.5379.Google Scholar
Welsh, K., Singer, J., and Heinz, U. W.. Initial state fluctuations in collisions between light and heavy ions. Phys. Rev., C94(2):024919, 2016, 1605.09418.Google Scholar
Weller, R. D. and Romatschke, P.. One fluid to rule them all: viscous hydrodynamic description of event-by-event central p+p, p+Pb and Pb+Pb collisions at Phys. Lett., B774:351356, 2017, 1701.07145.CrossRefGoogle Scholar
Glauber, R. J.. Lectures in Theoretical Physics, ed. WE Brittin and LG Dunham, New York: Interscience, 1:315, 1959.Google Scholar
Glauber, R. J.. Quantum optics and heavy ion physics. Nucl. Phys., A774:313, 2006, nucl-th/0604021.CrossRefGoogle Scholar
Aad, G. et al. Measurement of the inelastic proton-proton cross-section at with the ATLAS detector. Nature Commun., 2:463, 2011, 1104.0326.Google Scholar
Aaboud, M. et al. Measurement of the inelastic proton-proton cross section at with the ATLAS detector at the LHC. Phys. Rev. Lett., 117(18):182002, 2016, 1606.02625.CrossRefGoogle Scholar
Kharzeev, D. and Nardi, M.. Hadron production in nuclear collisions at RHIC and high density QCD. Phys. Lett., B507:121128, 2001, nucl-th/0012025.CrossRefGoogle Scholar
Kolb, P. F., Heinz, U. W., Huovinen, P., Eskola, K. J., and Tuominen, K.. Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics. Nucl. Phys., A696:197215, 2001, hep-ph/0103234.CrossRefGoogle Scholar
McLerran, L. D. and Venugopalan, R.. Computing quark and gluon distribution functions for very large nuclei. Phys. Rev., D49:22332241, 1994, hep-ph/9309289.Google Scholar
McLerran, L. D. and Venugopalan, R.. Gluon distribution functions for very large nuclei at small transverse momentum. Phys. Rev., D49:33523355, 1994, hep-ph/9311205.Google Scholar
Jalilian-Marian, J., Kovner, A., McLerran, L. D., and Weigert, Heribert. The Intrinsic glue distribution at very small x. Phys. Rev., D55:54145428, 1997, hep-ph/9606337.Google Scholar
Kovchegov, Y. V.. Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus. Phys. Rev., D54:54635469, 1996, hep-ph/9605446.Google Scholar
Kovner, A., McLerran, L. D., and Weigert, H.. Gluon production at high transverse momentum in the McLerran-Venugopalan model of nuclear structure functions. Phys. Rev., D52:38093814, 1995, hep-ph/9505320.Google Scholar
Ipp, A. and Müller, D.. Broken boost invariance in the Glasma via finite nuclei thickness. Phys. Lett., B771:7479, 2017, 1703.00017.CrossRefGoogle Scholar
Krasnitz, A. and Venugopalan, R.. The initial energy density of gluons produced in very high-energy nuclear collisions. Phys. Rev. Lett., 84:43094312, 2000, hep-ph/9909203.CrossRefGoogle ScholarPubMed
Lappi, T.. Production of gluons in the classical field model for heavy ion collisions. Phys. Rev., C67:054903, 2003, hep-ph/0303076.Google Scholar
Romatschke, P. and Venugopalan, R.. Collective non-Abelian instabilities in a melting color glass condensate. Phys. Rev. Lett., 96:062302, 2006, hep-ph/0510121.CrossRefGoogle Scholar
Romatschke, P. and Venugopalan, R.. The unstable glasma. Phys. Rev., D74:045011, 2006, hep-ph/0605045.Google Scholar
Fukushima, K. and Gelis, F.. The evolving glasma. Nucl. Phys., A874:108129, 2012, 1106.1396.CrossRefGoogle Scholar
Berges, J. and Schlichting, S.. The nonlinear glasma. Phys. Rev., D87(1):014026, 2013, 1209.0817.Google Scholar
Epelbaum, T. and Gelis, F.. Pressure isotropization in high energy heavy ion collisions. Phys. Rev. Lett., 111:232301, 2013, 1307.2214.CrossRefGoogle ScholarPubMed
Schenke, B., Tribedy, P., and Venugopalan, R.. Fluctuating glasma initial conditions and flow in heavy ion collisions. Phys. Rev. Lett., 108:252301, 2012, 1202.6646.CrossRefGoogle ScholarPubMed
Krasnitz, A., Nara, Y., and Venugopalan, R.. Gluon production in the color glass condensate model of collisions of ultrarelativistic finite nuclei. Nucl. Phys., A717:268290, 2003, hep-ph/0209269.CrossRefGoogle Scholar
Martin, A. D.. Proton structure, Partons, QCD, DGLAP and beyond. Acta Phys. Polon., B39:20252062, 2008, 0802.0161.Google Scholar
Kowalski, H. and Teaney, D.. An impact parameter dipole saturation model. Phys. Rev., D68:114005, 2003, hep-ph/0304189.Google Scholar
Rezaeian, A. H., Siddikov, M., Van de Klundert, M., and Venugopalan, R.. Analysis of combined HERA data in the Impact-Parameter dependent Saturation model. Phys. Rev., D87(3):034002, 2013, 1212.2974.Google Scholar
Schenke, B., Tribedy, P., and Venugopalan, R.. Event-by-event gluon multiplicity, energy density, and eccentricities in ultrarelativistic heavy-ion collisions. Phys. Rev., C86:034908, 2012, 1206.6805.Google Scholar
Khachatryan, V. et al. Transverse momentum and pseudorapidity distributions of charged hadrons in pp collisions at and 2.36 TeV. JHEP, 02:041, 2010, 1002.0621.CrossRefGoogle Scholar
Lappi, T.. Energy density of the glasma. Phys. Lett., B643:1116, 2006, hep-ph/0606207.CrossRefGoogle Scholar
Chen, G., Fries, R. J., Kapusta, J. I., and Li, Y.. Early time dynamics of gluon fields in high energy nuclear collisions. Phys. Rev., C92(6):064912, 2015, 1507.03524.Google Scholar
Jackson, J. D.. Classical Electrodynamics. Wiley, 1998.Google Scholar
Steinbauer, R.. The ultrarelativistic Reissner-Nordstrom field in the Colombeau algebra. J. Math. Phys., 38:16141622, 1997, gr-qc/9606059.CrossRefGoogle Scholar
Lousto, C. O. and Sanchez, N. G.. The Curved Shock Wave Space-time of Ultrarelativistic Charged Particles and Their Scattering. Int. J. Mod. Phys., A5:915, 1990.CrossRefGoogle Scholar
Grumiller, D. and Romatschke, P.. On the collision of two shock waves in AdS5. JHEP, 08:027, 2008, 0803.3226.CrossRefGoogle Scholar
Romatschke, P. and Hogg, J. D.. Pre-equilibrium radial flow from central shock-wave collisions in AdS5. JHEP, 04:048, 2013, 1301.2635.CrossRefGoogle Scholar
Taliotis, A.. Heavy ion collisions with transverse dynamics from evolving AdS geometries. JHEP, 09:102, 2010, 1004.3500.CrossRefGoogle Scholar
Avsar, E., Iancu, E., McLerran, L., and Triantafyllopoulos, D. N.. Shockwaves and deep inelastic scattering within the gauge/gravity duality. JHEP, 11:105, 2009, 0907.4604.CrossRefGoogle Scholar
Gubser, S. S., Pufu, S. S., and Yarom, A.. Entropy production in collisions of gravitational shock waves and of heavy ions. Phys. Rev., D78:066014, 2008, 0805.1551.Google Scholar
Khan, K. A. and Penrose, R.. Scattering of two impulsive gravitational plane waves. Nature, 229:185186, 1971.CrossRefGoogle ScholarPubMed
D’Eath, P. D. and Payne, P. N.. Gravitational radiation in high speed black hole collisions. 1. Perturbation treatment of the axisymmetric speed of light collision. Phys. Rev., D46:658674, 1992.Google Scholar
D’Eath, P. D. and Payne, P. N.. Gravitational radiation in high speed black hole collisions. 2. Reduction to two independent variables and calculation of the second order news function. Phys. Rev., D46:675693, 1992.Google Scholar
D’Eath, P. D. and Payne, P. N.. Gravitational radiation in high speed black hole collisions. 3. Results and conclusions. Phys. Rev., D46:694701, 1992.Google Scholar
Chesler, P. M. and Yaffe, L. G.. Holography and colliding gravitational shock waves in asymptotically AdS5 spacetime. Phys. Rev. Lett., 106:021601, 2011, 1011.3562.CrossRefGoogle ScholarPubMed
Fernández, D.. Towards collisions of inhomogeneous shockwaves in AdS. JHEP, 07:126, 2015, 1407.5628.CrossRefGoogle Scholar
Chesler, P. M. and Yaffe, L. G.. Holography and off-center collisions of localized shock waves. JHEP, 10:070, 2015, 1501.04644.CrossRefGoogle Scholar
Grozdanov, S. and van der Schee, W.. Coupling constant corrections in a holographic model of heavy ion collisions. Phys. Rev. Lett., 119(1):011601, 2017, 1610.08976.CrossRefGoogle Scholar
Yoshino, H. and Nambu, Y.. High-energy headon collisions of particles and hoop conjecture. Phys. Rev., D66:065004, 2002, gr-qc/0204060.Google Scholar
Stephanov, M. and Yin, Y.. Reversing a heavy-ion collision. 2014, 1404.5910.Google Scholar
van der Schee, W. and Schenke, B.. Rapidity dependence in holographic heavy ion collisions. Phys. Rev., C92(6):064907, 2015, 1507.08195.Google Scholar
Habich, M., Nagle, J. L., and Romatschke, P.. Particle spectra and HBT radii for simulated central nuclear collisions of C + C, Al + Al, Cu + Cu, Au + Au, and Pb + Pb from Eur. Phys. J., C75(1):15, 2015, 1409.0040.CrossRefGoogle Scholar
Teaney, D. and Yan, L.. Triangularity and dipole asymmetry in heavy ion collisions. Phys. Rev., C83:064904, 2011, 1010.1876.Google Scholar
Bhalerao, R. S., Luzum, M., and Ollitrault, J.-Y.. Determining initial-state fluctuations from flow measurements in heavy-ion collisions. Phys. Rev., C84:034910, 2011, 1104.4740.Google Scholar
Retinskaya, E., Luzum, M., and Ollitrault, J.-Y.. Constraining models of initial conditions with elliptic and triangular flow data. Phys. Rev., C89(1):014902, 2014, 1311.5339.Google Scholar
Lappi, T. and Venugopalan, R.. Universality of the saturation scale and the initial eccentricity in heavy ion collisions. Phys. Rev., C74:054905, 2006, nucl-th/0609021.Google Scholar
Song, H. and Heinz, U. W.. Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions. Phys. Rev., C77:064901, 2008, 0712.3715.Google Scholar
Molnar, E., Niemi, H., and Rischke, D. H.. Numerical tests of causal relativistic dissipative fluid dynamics. Eur. Phys. J., C65:615635, 2010, 0907.2583.CrossRefGoogle Scholar
Mendoza, M., Boghosian, B., Herrmann, H. J., and Succi, S.. Fast Lattice Boltzmann Solver for Relativistic Hydrodynamics. Phys. Rev. Lett., 105:014502, 2010, 0912.2913.CrossRefGoogle ScholarPubMed
Bozek, P.. Flow and interferometry in 3+1 dimensional viscous hydrodynamics. Phys. Rev., C85:034901, 2012, 1110.6742.Google Scholar
Del Zanna, L., Chandra, V., Inghirami, G., Rolando, V., Beraudo, A., De Pace, A., Pagliara, G., Drago, A., and Becattini, F.. Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP. Eur. Phys. J., C73:2524, 2013, 1305.7052.CrossRefGoogle Scholar
Luzum, M. and Romatschke, P.. Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at s(NN)**(1/2) = 200-GeV. Phys. Rev., C78:034915, 2008, 0804.4015. [Erratum: Phys. Rev.C79,039903(2009)].Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, Brian P.. Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, New York, NY, USA, 3 edition, 2007.Google Scholar
Kurganov, A. and Tadmor, E.. New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations. Journal of Computational Physics, 160:241282, May 2000.CrossRefGoogle Scholar
Schenke, B., Jeon, S., and Gale, C.. (3+1)D hydrodynamic simulation of relativistic heavy-ion collisions. Phys. Rev., C82:014903, 2010, 1004.1408.Google Scholar
Naidoo, R. and Baboolal, S.. Application of the kurganov-levy semi-discrete numerical scheme to hyperbolic problems with nonlinear source terms. Future Generation Comp. Syst., 20(3):465473, 2004.CrossRefGoogle Scholar
Romatschke, P., Mendoza, M., and Succi, S.. A fully relativistic lattice Boltzmann algorithm. Phys. Rev., C84:034903, 2011, 1106.1093.Google Scholar
Mendoza, M., Karlin, I., Succi, S., and Herrmann, H. J.. Relativistic Lattice Boltzmann Model with Improved Dissipation. Phys. Rev., D87(6):065027, 2013, 1301.3423.Google Scholar
Ambrus, V. E. and Blaga, R.. Relativistic rotating Boltzmann gas using the tetrad formalism. Analele Univ. Timisoara (Stiinte Fiz.), 58:89108, 2015, 1512.03330.Google Scholar
Succi, S., Mendoza, M., Mohseni, F., and Karlin, I.. Relativistic lattice kinetic theory: Recent developments and future prospects. European Physical Journal Special Topics, 223, October 2014.CrossRefGoogle Scholar
Velasco, A. M., Muñoz, J. D., and Mendoza, M.. Lattice Boltzmann model in curvilinear coordinates for the study of the vibrational modes of a trumpet. ArXiv e-prints, May 2017, 1705.01801.Google Scholar
Peng, G., Xi, H., Duncan, C., and Chou, S.-H.. Lattice boltzmann method on irregular meshes. Phys. Rev. E, 58:R4124R4127, Oct 1998.CrossRefGoogle Scholar
Ubertini, S., Bella, G., and Succi, S.. Lattice Boltzmann method on unstructured grids: Further developments. Phys. Rev., E68(1):016701, July 2003.Google Scholar
Brewer, J., Mendoza, M., Young, R. E., and Romatschke, P.. Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas. Phys. Rev., A93(1):013618, 2016, 1507.05975.CrossRefGoogle Scholar
Ansumali, S. and Karlin, I. V.. Entropy function approach to the lattice boltzmann method. Journal of Statistical Physics, 107(1):291308, Apr 2002.CrossRefGoogle Scholar
Frapolli, N., Chikatamarla, S. S., and Karlin, I. V.. Entropic lattice boltzmann model for compressible flows. Phys. Rev. E, 92:061301, Dec 2015.CrossRefGoogle ScholarPubMed
Mohseni, F., Mendoza, M., Succi, S., and Herrmann, H. J.. Lattice boltzmann model for ultrarelativistic flows. Phys. Rev. D, 87:083003, Apr 2013.CrossRefGoogle Scholar
Mohseni, F., Mendoza, M., Succi, S., and Herrmann, H. J.. Relativistic effects on the Richtmyer-Meshkov instability. Phys. Rev., D90(12):125028, December 2014, 1309.0347.Google Scholar
Bantilan, H. and Romatschke, P.. Simulation of black hole collisions in asymptotically anti–de Sitter spacetimes. Phys. Rev. Lett., 114(8):081601, 2015, 1410.4799.CrossRefGoogle ScholarPubMed
Gelis, F. and Jalilian-Marian, J.. Photon production in high-energy proton nucleus collisions. Phys. Rev., D66:014021, 2002, hep-ph/0205037.Google Scholar
Arleo, F. et al. Hard probes in heavy-ion collisions at the LHC: Photon physics in heavy ion collisions at the LHC. 2004, hep-ph/0311131.Google Scholar
Martinez, M. and Strickland, M.. Pre-equilibrium dilepton production from an anisotropic quark-gluon plasma. Phys. Rev., C78:034917, 2008, 0805.4552.Google Scholar
Martinez, M. and Strickland, M.. Suppression of forward dilepton production from an anisotropic quark-gluon plasma. Eur. Phys. J., C61:905913, 2009, 0808.3969.CrossRefGoogle Scholar
Rebhan, A. and Steineder, D.. Electromagnetic signatures of a strongly coupled anisotropic plasma. JHEP, 08:153, 2011, 1106.3539.CrossRefGoogle Scholar
Oliva, L., Ruggieri, M., Plumari, S., Scardina, F., Peng, G. X., and Greco, V.. Photons from the Early Stages of Relativistic Heavy Ion Collisions. Phys. Rev., C96(1):014914, 2017, 1703.00116.Google Scholar
Berges, J., Reygers, K., Tanji, N., and Venugopalan, R.. Parametric estimate of the relative photon yields from the glasma and the quark-gluon plasma in heavy-ion collisions. Phys. Rev., C95(5):054904, 2017, 1701.05064.Google Scholar
Jeon, S. and Yaffe, L. G.. From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory. Phys. Rev., D53:57995809, 1996, hep-ph/9512263.Google Scholar
Dobado, A., Llanes-Estrada, F. J., and Torres-Rincon, J. M.. Bulk viscosity of low-temperature strongly interacting matter. Phys. Lett., B702:4348, 2011, 1103.0735.CrossRefGoogle Scholar
Li, B.-C. and Huang, M.. Thermodynamic properties and bulk viscosity near phase transition in the Z(2) and O(4) models. Phys. Rev., D80:034023, 2009, 0903.3650.Google Scholar
Monnai, A., Mukherjee, S., and Yin, Y.. Phenomenological consequences of enhanced bulk viscosity near the QCD critical point. Phys. Rev., C95(3):034902, 2017, 1606.00771.Google Scholar
Huovinen, P. and Petersen, H.. Particlization in hybrid models. Eur. Phys. J., A48:171, 2012, 1206.3371.CrossRefGoogle Scholar
Ruuskanen, P. V.. Transverse hydrodynamics with a first order phase transition in very high-energy nuclear collisions. Acta Phys. Polon., B18:551, 1987.Google Scholar
Rischke, D. H. and Gyulassy, M.. The time delay signature of quark - gluon plasma formation in relativistic nuclear collisions. Nucl. Phys., A608:479512, 1996, nucl-th/9606039.CrossRefGoogle Scholar
Cooper, F. and Frye, G.. Comment on the single particle distribution in the hydrodynamic and statistical thermodynamic models of multiparticle production. Phys. Rev., D10:186, 1974.Google Scholar
Baier, R., Romatschke, P., and Wiedemann, U. A.. Dissipative hydrodynamics and heavy ion collisions. Phys. Rev., C73:064903, 2006, hep-ph/0602249.Google Scholar
Luzum, M. and Ollitrault, J.-Y.. Constraining the viscous freeze-out distribution function with data obtained at the BNL Relativistic Heavy Ion Collider (RHIC). Phys. Rev., C82:014906, 2010, 1004.2023.Google Scholar
Pratt, S. and Torrieri, G.. Coupling relativistic viscous hydrodynamics to Boltzmann descriptions. Phys. Rev., C82:044901, 2010, 1003.0413.Google Scholar
van der Schee, W., Romatschke, P., and Pratt, S.. Fully Dynamical Simulation of Central Nuclear Collisions. Phys. Rev. Lett., 111(22):222302, 2013, 1307.2539.CrossRefGoogle ScholarPubMed
Monnai, A. and Hirano, T.. Effects of bulk viscosity at freezeout. Phys. Rev., C80:054906, 2009, 0903.4436.Google Scholar
Novak, J., Novak, K., Pratt, S., Vredevoogd, J., Coleman-Smith, C., and Wolpert, R.. Determining fundamental properties of matter created in ultrarelativistic heavy-ion collisions. Phys. Rev., C89(3):034917, 2014, 1303.5769.Google Scholar
Bugaev, K. A., Gorenstein, Mark I., and Greiner, W.. Particle freezeout and discontinuities in relativistic hydrodynamics. J. Phys., G25:21472160, 1999, nucl-th/9906088.CrossRefGoogle Scholar
Molnar, E., Csernai, L. P., Magas, V. K., Nyiri, A., and Tamosiunas, K.. Covariant description of kinetic freeze out through a finite space-like layer. Phys. Rev., C74:024907, 2006, nucl-th/0503047.Google Scholar
Zhang, B.. ZPC 1.0.1: A Parton cascade for ultrarelativistic heavy ion collisions. Comput. Phys. Commun., 109:193206, 1998, nucl-th/9709009.CrossRefGoogle Scholar
Bass, S. A. et al. Microscopic models for ultrarelativistic heavy ion collisions. Prog. Part. Nucl. Phys., 41:255369, 1998, nucl-th/9803035. [Prog. Part. Nucl. Phys.41, 225 (1998)].CrossRefGoogle Scholar
Molnar, D. and Gyulassy, M.. New solutions to covariant nonequilibrium dynamics. Phys. Rev., C62:054907, 2000, nucl-th/0005051.Google Scholar
Xu, Z. and Greiner, C.. Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade. Phys. Rev., C71:064901, 2005, hep-ph/0406278.Google Scholar
Poskanzer, A. M. and Voloshin, S. A.. Methods for analyzing anisotropic flow in relativistic nuclear collisions. Phys. Rev., C58:16711678, 1998, nucl-ex/9805001.Google Scholar
Heinz, U., Qiu, Z., and Shen, C.. Fluctuating flow angles and anisotropic flow measurements. Phys. Rev., C87(3):034913, 2013, 1302.3535.Google Scholar
Heinz, U. and Snellings, R.. Collective flow and viscosity in relativistic heavy-ion collisions. Ann. Rev. Nucl. Part. Sci., 63:123151, 2013, 1301.2826.CrossRefGoogle Scholar
Voloshin, S. and Zhang, Y.. Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions. Z. Phys., C70:665672, 1996, hep-ph/9407282.Google Scholar
Alver, B. H., Gombeaud, C., Luzum, M., and Ollitrault, J.-Y.. Triangular flow in hydrodynamics and transport theory. Phys. Rev., C82:034913, 2010, 1007.5469.Google Scholar
Snellings, R.. Elliptic flow: A brief review. New J. Phys., 13:055008, 2011, 1102.3010.CrossRefGoogle Scholar
Luzum, M.. Elliptic flow at energies available at the CERN Large Hadron Collider: Comparing heavy-ion data to viscous hydrodynamic predictions. Phys. Rev., C83:044911, 2011, 1011.5173.Google Scholar
Alver, B. et al. Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions. Phys. Rev., C77:014906, 2008, 0711.3724.Google Scholar
Romatschke, P.. Light-heavy ion collisions: A window into pre-equilibrium QCD dynamics? Eur. Phys. J., C75(7):305, 2015, 1502.04745.CrossRefGoogle Scholar
Bilandzic, A., Snellings, R., and Voloshin, S.. Flow analysis with cumulants: Direct calculations. Phys. Rev., C83:044913, 2011, 1010.0233.Google Scholar
Borghini, N., Mai Dinh, P., and Ollitrault, J.-Y.. A new method for measuring azimuthal distributions in nucleus-nucleus collisions. Phys. Rev., C63:054906, 2001, nucl-th/0007063.Google Scholar
Borghini, N., Dinh, P. M., and Ollitrault, J.-Y.. Flow analysis from multiparticle azimuthal correlations. Phys. Rev., C64:054901, 2001, nucl-th/0105040.Google Scholar
Bilandzic, A.. Anisotropic flow measurements in ALICE at the large hadron collider. PhD thesis, Utrecht U., 2012.Google Scholar
Brown, R. H. and Twiss, R. Q.. Correlation between Photons in two Coherent Beams of Light. Nature, 177:2729, January 1956.CrossRefGoogle Scholar
Lisa, M. A., Pratt, S., Soltz, R., and Wiedemann, U.. Femtoscopy in relativistic heavy ion collisions. Ann. Rev. Nucl. Part. Sci., 55:357402, 2005, nucl-ex/0505014.CrossRefGoogle Scholar
Soff, S., Bass, S. A., and Dumitru, A.. Pion interferometry at RHIC: Probing a thermalized quark gluon plasma? Phys. Rev. Lett., 86:39813984, 2001, nucl-th/0012085.CrossRefGoogle Scholar
Hirano, T. and Tsuda, K.. Collective flow and HBT radii from a full 3-D hydrodynamic model with early chemical freezeout. Nucl. Phys., A715:821824, 2003, nucl-th/0208068.CrossRefGoogle Scholar
Pratt, S.. Resolving the HBT puzzle in relativistic heavy ion collision. Phys. Rev. Lett., 102:232301, 2009, 0811.3363.CrossRefGoogle Scholar
Becattini, F., Gazdzicki, M., Keranen, A., Manninen, J., and Stock, R.. Chemical equilibrium in nucleus nucleus collisions at relativistic energies. Phys. Rev., C69:024905, 2004, hep-ph/0310049.Google Scholar
Braun-Munzinger, P., Stachel, J., Wessels, J. P., and Xu, N.. Thermal equilibration and expansion in nucleus-nucleus collisions at the AGS. Phys. Lett., B344:4348, 1995, nucl-th/9410026.CrossRefGoogle Scholar
Baier, R. and Romatschke, P.. Causal viscous hydrodynamics for central heavy-ion collisions. Eur. Phys. J., C51:677687, 2007, nucl-th/0610108.CrossRefGoogle Scholar
Huovinen, P. and Ruuskanen, P. V.. Hydrodynamic models for heavy ion collisions. Ann. Rev. Nucl. Part. Sci., 56:163206, 2006, nucl-th/0605008.CrossRefGoogle Scholar
Borghini, N. and Ollitrault, J.-Y.. Momentum spectra, anisotropic flow, and ideal fluids. Phys. Lett., B642:227231, 2006, nucl-th/0506045.CrossRefGoogle Scholar
Schukraft, J.. QM2017: Status and key open questions in ultra-relativistic heavy-ion physics. Nucl. Phys., A967:110, 2017, 1705.02646.CrossRefGoogle Scholar
Zajc, W. A.. The way forward – closing remarks at quark matter 2017. Nucl. Phys., A967:265272, 2017, 1707.01993.CrossRefGoogle Scholar
Niemi, H., Eskola, K. J., and Paatelainen, R.. Event-by-event fluctuations in a perturbative QCD + saturation + hydrodynamics model: Determining QCD matter shear viscosity in ultrarelativistic heavy-ion collisions. Phys. Rev., C93(2):024907, 2016, 1505.02677.Google Scholar
Werner, K., Karpenko, Iu., Pierog, T., Bleicher, M., and Mikhailov, K.. Event-by-Event Simulation of the Three-Dimensional Hydrodynamic Evolution from Flux Tube Initial Conditions in Ultrarelativistic Heavy Ion Collisions. Phys. Rev., C82:044904, 2010, 1004.0805.Google Scholar
Bozek, P.. Bulk and shear viscosities of matter created in relativistic heavy-ion collisions. Phys. Rev., C81:034909, 2010, 0911.2397.Google Scholar
Alqahtani, M., Nopoush, M., Ryblewski, R., and Strickland, M.. (3+1)D Quasiparticle anisotropic hydrodynamics for ultrarelativistic heavy-ion collisions. Phys. Rev. Lett., 119(4):042301, 2017, 1703.05808.CrossRefGoogle Scholar
Shen, C., Qiu, Z., Song, H., Bernhard, J., Bass, S., and Heinz, U.. The iEBE-VISHNU code package for relativistic heavy-ion collisions. Comput. Phys. Commun., 199:6185, 2016, 1409.8164.CrossRefGoogle Scholar
Vredevoogd, J. and Pratt, S.. Universal flow in the first stage of relativistic heavy ion collisions. Phys. Rev., C79:044915, 2009, 0810.4325.Google Scholar
Keegan, L., Kurkela, A., Mazeliauskas, A., and Teaney, D.. Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution. JHEP, 08:171, 2016, 1605.04287.CrossRefGoogle Scholar
Adler, S. S. et al. Systematic studies of the centrality and s(NN)**(1/2) dependence of the d E(T) / d eta and d (N(ch) / d eta in heavy ion collisions at mid-rapidity. Phys. Rev., C71:034908, 2005, nucl-ex/0409015. [Erratum: Phys. Rev.C71,049901(2005)].Google Scholar
Aamodt, K. et al. Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at Phys. Rev. Lett., 106:032301, 2011, 1012.1657.CrossRefGoogle Scholar
Abelev, B. I. et al. Systematic measurements of identified particle spectra in pp, d + Au and Au+Au collisions from STAR. Phys. Rev., C79:034909, 2009, 0808.2041.Google Scholar
Abelev, B. et al. Centrality dependence of π, K, p production in Pb-Pb collisions at Rev., C88:044910, 2013, 1303.0737.Google Scholar
Adler, S. S. et al. Identified charged particle spectra and yields in Au+Au collisions at S(NN)**1/2 = 200-GeV. Phys. Rev., C69:034909, 2004, nucl-ex/0307022.Google Scholar
Aggarwal, M. M. et al. Scaling properties at freeze-out in relativistic heavy ion collisions. Phys. Rev., C83:034910, 2011, 1008.3133.Google Scholar
Romatschke, P.. Causal viscous hydrodynamics for central heavy-ion collisions. II. Meson spectra and HBT radii. Eur. Phys. J., C52:203209, 2007, nucl-th/0701032.CrossRefGoogle Scholar
Ryu, S., Paquet, J. F., Shen, C., Denicol, G. S., Schenke, B., Jeon, S., and Gale, C.. Importance of the Bulk Viscosity of QCD in Ultrarelativistic Heavy-Ion Collisions. Phys. Rev. Lett., 115(13):132301, 2015, 1502.01675.CrossRefGoogle ScholarPubMed
Abelev, B. et al. Anisotropic flow of charged hadrons, pions and (anti-) protons measured at high transverse momentum in Pb-Pb collisions at Phys. Lett., B719:1828, 2013, 1205.5761.CrossRefGoogle Scholar
Aamodt, K. et al. Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at Phys. Rev. Lett., 107:032301, 2011, 1105.3865.CrossRefGoogle Scholar
Bernhard, J. E., Moreland, J. S., Bass, S. A., Liu, J., and Heinz, U.. Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium. Phys. Rev., C94(2):024907, 2016, 1605.03954.Google Scholar
Aad, G. et al. Measurement of the distributions of event-by-event flow harmonics in lead-lead collisions at = 2.76 TeV with the ATLAS detector at the LHC. JHEP, 11:183, 2013, 1305.2942.Google Scholar
Gale, C., Jeon, S., Schenke, B., Tribedy, P., and Venugopalan, R.. Event-by-event anisotropic flow in heavy-ion collisions from combined Yang-Mills and viscous fluid dynamics. Phys. Rev. Lett., 110(1):012302, 2013, 1209.6330.CrossRefGoogle ScholarPubMed
Aamodt, K. et al. Two-pion Bose-Einstein correlations in central Pb-Pb collisions at Lett., B696:328337, 2011, 1012.4035.Google Scholar
Abelev, B. I. et al. Pion interferometry in Au+Au and Cu+Cu collisions at RHIC. Phys. Rev., C80:024905, 2009, 0903.1296.Google Scholar
Adare, A. et al. Quadrupole anisotropy in dihadron azimuthal correlations in central d+Au collisions at Phys. Rev. Lett., 111(21):212301, 2013, 1303.1794.CrossRefGoogle Scholar
Adare, A. et al. Measurements of elliptic and triangular flow in high-multiplicity 3He+Au collisions at Phys. Rev. Lett., 115(14):142301, 2015, 1507.06273.CrossRefGoogle Scholar
Aidala, C. et al. Measurement of long-range angular correlations and azimuthal anisotropies in high-multiplicity p+Au collisions at 2016, 1609.02894.Google Scholar
Nagle, J. L. and Zajc, W. A.. Small system collectivity in relativistic hadron and nuclear collisions. 2018, 1801.03477.Google Scholar
Dusling, K., Li, W., and Schenke, B.. Novel collective phenomena in high-energy proton–proton and proton–nucleus collisions. Int. J. Mod. Phys., E25(01):1630002, 2016, 1509.07939.CrossRefGoogle Scholar
Bozek, P.. Collective flow in p-Pb and d-Pd collisions at TeV energies. Phys. Rev., C85:014911, 2012, 1112.0915.Google Scholar
Schenke, B. and Venugopalan, R.. Eccentric protons? Sensitivity of flow to system size and shape in p+p, p+Pb and Pb+Pb collisions. Phys. Rev. Lett., 113:102301, 2014, 1405.3605.CrossRefGoogle Scholar
Kozlov, I., Luzum, M., Denicol, G., Jeon, S., and Gale, C.. Transverse momentum structure of pair correlations as a signature of collective behavior in small collision systems. 2014, 1405.3976.CrossRefGoogle Scholar
Werner, K., Guiot, B., Karpenko, Iu., and Pierog, T.. A unified description of the reaction dynamics from pp to pA to AA collisions. Nucl. Phys., A931:8391, 2014, 1411.1048.CrossRefGoogle Scholar
Bozek, P. and Broniowski, W.. Hydrodynamic modeling of 3 He–Au collisions at Phys. Lett., B747:135138, 2015, 1503.00468.CrossRefGoogle Scholar
Mäntysaari, H., Schenke, B., Shen, C., and Tribedy, P.. Imprints of fluctuating proton shapes on flow in proton-lead collisions at the LHC. Phys. Lett., B772: 681–686, 2017, 1705.03177.Google Scholar
Abelev, B. B. et al. Multiplicity dependence of pion, kaon, proton and lambda production in p-Pb collisions at Lett., B728:2538, 2014, 1307.6796.Google Scholar
Aad, G. et al. Measurement of long-range pseudorapidity correlations and azimuthal harmonics in proton-lead collisions with the ATLAS detector. Phys. Rev., C90(4):044906, 2014, 1409.1792.Google Scholar
Aidala, C. et al. Measurements of azimuthal anisotropy and charged-particle multiplicity in d+Au collisions at and 19.6 GeV. 2017, 1708.06983.Google Scholar
Bozek, P. and Broniowski, W.. Collective flow in ultrarelativistic 3He-Au collisions. Phys. Lett., B739:308312, 2014, 1409.2160.CrossRefGoogle Scholar
Orjuela Koop, J. D., Belmont, R., Yin, P., and Nagle, J. L.. Exploring the beam energy dependence of flow-like signatures in small system d+Au collisions. Phys. Rev., C93(4):044910, 2016, 1512.06949.Google Scholar
Adam, J. et al. Two-pion femtoscopy in p-Pb collisions at Phys. Rev., C91:034906, 2015, 1502.00559.Google Scholar
Aad, G. et al. Observation of long-range elliptic anisotropies in and 2.76 TeV pp collisions with the ATLAS detector. 2015, 1509.04776.Google Scholar
Khachatryan, V. et al. Measurement of long-range near-side two-particle angular correlations in pp collisions at Phys. Rev. Lett., 116(17):172302, 2016, 1510.03068.CrossRefGoogle Scholar
Khachatryan, V. et al. Evidence for collectivity in pp collisions at the LHC. Phys. Lett., B765:193220, 2017, 1606.06198.CrossRefGoogle Scholar
Aaboud, M. et al. Measurements of long-range azimuthal anisotropies and associated Fourier coefficients for pp collisions at and 13 TeV and p+Pb collisions at with the ATLAS detector. 2016, 1609.06213.Google Scholar
Adam, J. et al. Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions. Nature Phys., 13:535539, 2017, 1606.07424.Google Scholar
Schenke, B., Schlichting, S., Tribedy, P., and Venugopalan, R.. Mass ordering of spectra from fragmentation of saturated gluon states in high multiplicity proton-proton collisions. Phys. Rev. Lett., 117(16):162301, 2016, 1607.02496.CrossRefGoogle ScholarPubMed
Iancu, E. and Rezaeian, A. H.. Elliptic flow from color-dipole orientation in pp and pA collisions. Phys. Rev., D95(9):094003, 2017, 1702.03943.Google Scholar
Blok, B., Jäkel, C. D., Strikman, M., and Wiedemann, U. A.. Collectivity from interference. 2017, 1708.08241.CrossRefGoogle Scholar
Prasad, S. K., Roy, V., Chattopadhyay, S., and Chaudhuri, A. K.. Elliptic flow (v2) in pp collisions at energies available at the CERN Large Hadron Collider: A hydrodynamical approach. Phys. Rev., C82:024909, 2010, 0910.4844.Google Scholar
Ortona, G., Denicol, G. S., Ph. Mota, , and Kodama, T.. Elliptic flow in high multiplicity proton-proton collisions at as a signature of deconfinement and quantum energy density fluctuations. 2009, 0911.5158.Google Scholar
Werner, K., Karpenko, Iu., and Pierog, T.. The “Ridge” in Proton-Proton Scattering at 7 TeV. Phys. Rev. Lett., 106:122004, 2011,1011.0375.CrossRefGoogle Scholar
Bozek, P.. Elliptic flow in proton-proton collisions at Phys. J., C71:1530, 2011, 1010.0405.Google Scholar
Bianchi, L.. Strangeness production as a function of charged particle multiplicity in proton–proton collisions. Nucl. Phys., A956:777780, 2016, 1604.06736.CrossRefGoogle Scholar
Habich, M., Miller, G. A., Romatschke, P., and Xiang, W.. Testing hydrodynamic descriptions of p+p collisions at Phys. J., C76(7):408, 2016, 1512.05354.Google Scholar
Bandurin, D. A., Torre, I., Kumar, R. K., Ben Shalom, M., Tomadin, A., Principi, A., Auton, G. H., Khestanova, E., Novoselov, K. S., Grigorieva, I. V., Ponomarenko, L. A., Geim, A. K., and Polini, M.. Negative local resistance caused by viscous electron backflow in graphene. Science, 351:10551058, March 2016, 1509.04165.CrossRefGoogle ScholarPubMed
Cao, C., Elliott, E., Joseph, J., Wu, H., Petricka, J., Schäfer, T., and Thomas, J. E.. Universal Quantum Viscosity in a Unitary Fermi Gas. Science, 331:58, 2011, 1007.2625.CrossRefGoogle Scholar
Rameau, J. D., Reber, T. J., Yang, H.-B., Akhanjee, S., Gu, G. D., Johnson, P. D., and Campbell, S.. Nearly perfect fluidity in a high-temperature superconductor. Phys. Rev. B, 90:134509, Oct 2014.CrossRefGoogle Scholar
Goldschmidt, A., Qiu, Z., Shen, C., and Heinz, U.. Collision geometry and flow in uranium + uranium collisions. Phys. Rev., C92(4):044903, 2015, 1507.03910.Google Scholar
Adare, A. et al. Azimuthally anisotropic emission of low-momentum direct photons in Au+Au collisions at Phys. Rev., C94(6):064901, 2016, 1509.07758.Google Scholar
Hongo, M., Hirono, Y., and Hirano, T.. Anomalous-hydrodynamic analysis of charge-dependent elliptic flow in heavy-ion collisions. Phys. Lett., B775:266270, 2017, 1309.2823.CrossRefGoogle Scholar
Roy, V., Pu, S., Rezzolla, L., and Rischke, D.. Analytic Bjorken flow in one-dimensional relativistic magnetohydrodynamics. Phys. Lett., B750:4552, 2015, 1506.06620.CrossRefGoogle Scholar
Arnold, P., Romatschke, P., and van der Schee, W.. Absence of a local rest frame in far from equilibrium quantum matter. JHEP, 10:110, 2014, 1408.2518.CrossRefGoogle Scholar
Larkoski, A. J., Marzani, S., and Thaler, J.. Sudakov safety in perturbative QCD. Phys. Rev., D91(11):111501, 2015, 1502.01719.Google Scholar
Berges, J., Borsanyi, Sz., Sexty, D., and Stamatescu, I. O.. Lattice simulations of real-time quantum fields. Phys. Rev., D75:045007, 2007, hep-lat/0609058.Google Scholar
Alexandru, A., Basar, G., Bedaque, P. F., and Ridgway, G. W.. Schwinger-Keldysh formalism on the lattice: A faster algorithm and its application to field theory. Phys. Rev., D95(11):114501, 2017, 1704.06404.Google Scholar
Kajantie, K., Louko, J., and Tahkokallio, T.. Gravity dual of conformal matter collisions in 1+1 dimensions. Phys. Rev., D77:066001, 2008, 0801.0198.Google Scholar
Inamuro, T., Ogata, T., Tajima, S., and Konishi, N.. A lattice boltzmann method for incompressible two-phase flows with large density differences. Journal of Computational Physics, 198(2):628 – 644, 2004.CrossRefGoogle Scholar
Hoang, T. F. and Cork, B.. Partition temperature and energy conservation of particle production. Zeitschrift für Physik C Particles and Fields, 34(3):385390, 1987.CrossRefGoogle Scholar
Becattini, F. and Passaleva, G.. Statistical hadronization model and transverse momentum spectra of hadrons in high-energy collisions. Eur. Phys. J., C23: 551583, 2002, hep-ph/0110312.CrossRefGoogle Scholar
Ferroni, L. and Becattini, F.. Statistical hadronization with exclusive channels in e+ e annihilation. Eur. Phys. J., C71:1824, 2011, 1109.5185.CrossRefGoogle Scholar
Nagle, J. L., Belmont, R., Hill, K., Koop, J. O., Perepelitsa, D. V., Yin, Pengqi, Lin, Zi-Wei, and McGlinchey, Darren. Are minimal conditions for collectivity met in e+ e collisions? 2017, 1707.02307.Google Scholar
Bonanos, S.. Riemann geometry & tensor calculus (RGTC). http://www.inp.demokritos.gr/ sbonano/RGTC/, version 3.8.9 (2013).Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Paul Romatschke, University of Colorado Boulder, Ulrike Romatschke, National Center for Atmospheric Research, Boulder, Colorado
  • Book: Relativistic Fluid Dynamics In and Out of Equilibrium
  • Online publication: 29 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108651998.011
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Paul Romatschke, University of Colorado Boulder, Ulrike Romatschke, National Center for Atmospheric Research, Boulder, Colorado
  • Book: Relativistic Fluid Dynamics In and Out of Equilibrium
  • Online publication: 29 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108651998.011
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Paul Romatschke, University of Colorado Boulder, Ulrike Romatschke, National Center for Atmospheric Research, Boulder, Colorado
  • Book: Relativistic Fluid Dynamics In and Out of Equilibrium
  • Online publication: 29 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108651998.011
Available formats
×