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Prospective Merger Between Car-Parrinello and Lattice Boltzmann Methods for Quantum Many-Body Simulations

Published online by Cambridge University Press:  20 August 2015

Sauro Succi  and
Silvia Palpacelli
Sauro Succi*
Affiliation:
Istituto Applicazioni Calcolo, CNR, via dei Taurini 19, 00185 Roma, Italy Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität Freiburg Albertstraβe 19, D-79104 Freiburg i.Br., Germany
Silvia Palpacelli*
Affiliation:
Numidia s.r.l, via Berna 31, 00144 Roma, Italy
*
Corresponding author.Email:[email protected]
Email:[email protected]
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Abstract

Formal analogies between the Car-Parrinello (CP) ab-initio molecular dynamics for quantum many-body systems, and the Lattice Boltzmann (LB) method for classical and quantum fluids, are pointed out. A theoretical scenario, whereby the quantum LB would be coupled to the CP framework to speed-up many-body quantum simulations, is also discussed, together with accompanying considerations on the computational efficiency of the prospective CP-LB scheme.

Keywords

31.15.-p47.11.-jQuantum many-body problemsCar-Parrinello ab-initio molecular dynamicslattice Boltzmann method
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1137 - 1151
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Car, R., and Parrinello, M., Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett., 55 (1985), 2471–2474.Google Scholar
[2]Benzi, R., Succi, S., and Vergassola, M., The lattice Boltzmann equation: theory and applications, Phys. Rep., 222 (1992), 145–197.Google Scholar
[3]Succi, S., Lattice Boltzmann across scales: from turbulence to DNA translocation, Euro. Phys. J. B., 64 (2008), 471–479.CrossRefGoogle Scholar
[4]Mendoza, M., Boghosian, B. M., Herrmann, H. J., and Succi, S., Fast lattice Boltzmann solver for relativistic hydrodynamics, Phys. Rev. Lett., 105 (2010), 014502.Google Scholar
[5]Hohenberg, P., and Kohn, W., Inhomogeneous electron gas, Phys. Rev., 136 (1964), B864–B871.Google Scholar
[6]Kohn, W., and Sham, L. J., Self-consistent equations including exchange and correlation effects, Phys. Rev., 140 (1965), A1133–A1138.Google Scholar
[7]Qian, Y. H., D’Humieres, D., and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), 479–484.CrossRefGoogle Scholar
[8]Bhatnagar, P. L., Gross, E., and Krook, M., A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), 511–525.Google Scholar
[9]Tuckerman, M., and Parrinello, M, Integrating the Car-Parrinello equations I. basic integration techniques, J. Chem. Phys., 101 (1994), 1302–1315.Google Scholar
[10]Tuckerman, M., and Parrinello, M, Integrating the Car-Parrinello equations II. multiple time-scale techniques, J. Chem. Phys., 101 (1994), 1316–1329.Google Scholar
[11]Boghosian, B. M., and Taylor, W., Quantum lattice-gas model for the many-particle Schrödinger equation in d dimensions, Phys. Rev. E., 57 (1998), 54–66.Google Scholar
[12]Yepez, J., and Boghosian, B. M., An efficient and accurate quantum lattice-gas model for the many-body Schrodinger wave equation, Comput. Phys. Commun., 146 (2002), 280–294.Google Scholar
[13]Succi, S., and Benzi, R., Lattice Boltzmann equation for quantum mechanics, Phys. D., 69 (1993), 327–332.CrossRefGoogle Scholar
[14]Succi, S., Numerical solution of the Schrödinger equation using discrete kinetic theory, Phys. Rev. E., 53 (1996), 1969–1975.Google Scholar
[15]Landau, L., and Lifshitz, E., Relativistic Quantum Field Theory, Pergamon, Oxford, 1960.Google Scholar
[16]Palpacelli, S., and Succi, S., The quantum lattice Boltzmann equation: recent developments, Commun. Comput. Phys., 4 (2008), 980–1007.Google Scholar
[17]Dellar, P., and Lapitski, D., APS March Meeting, Y22012, 2010.Google Scholar
[18]Palpacelli, S., and Succi, S., Numerical validation of the quantum lattice Boltzmann scheme in two and three dimensions, Phys. Rev. E., 75 (2007), 066704.Google Scholar
[19]Dellar, P., Lapitski, D., Palpacelli, S., and Succi, S., in preparation.Google Scholar
[20]Dellar, P., and Lapitski, D., in preparation.Google Scholar
[21]Palpacelli, S., Succi, S., and Spigler, R., Ground-state computation of Bose-Einstein condensates by an imaginary-time quantum lattice Boltzmann scheme, Phys. Rev. E., 76 (2007), 036712.Google Scholar
[22]Ahlrichs, P., and Dunweg, B., Simulation of a single polymer chain in solution by combining lattice Boltzmann and molecular dynamics, J. Chem. Phys., 11 (1999), 8225–8239.Google Scholar
[23]Fyta, M. G., Melchionna, S., Kaxiras, E., and Succi, S., Multiscale coupling of molecular dynamics and hydrodynamics: application to DNA translocation through a nanopore, Multiscale. Model. Simul., 5 (2006), 1156–1173.Google Scholar
[24] S. S Chikatamarla, and Karlin, I. V., Entropy and Galilean invariance of lattice Boltzmann theories, Phys. Rev. Lett., 97 (2006), 190601.Google Scholar
[25]Succi, S., Amati, G., and Piva, R., Massively parallel lattice Boltzmann simulation of turbulent channel flow, Int. J. Mod. Phys. C., 8 (1997), 869–877.Google Scholar
[26]Bernaschi, M., Melchionna, S., Succi, S., Fyta, M., Kaxiras, E., and Sircar, J. K., MUPHY: a parallel multi physics/scale code for high performance bio-fluidic simulations, Comput. Phys. Commun., 180 (2009), 1495–1502.CrossRefGoogle Scholar
[27]Tölke, J., Freudiger, S., and Krafczyc, M., An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations, Comput. Fluids., 35 (2006), 820–830.CrossRefGoogle Scholar