Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T19:41:07.189Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

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

[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