A complete quasiclassical map for the dynamics of interacting fermions
Abstract
We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. In conclusion, the numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.
- Authors:
-
- Univ. of California, Berkeley, CA (United States); Tel Aviv Univ., Tel Aviv (Israel)
- Univ. of California, Berkeley, CA (United States)
- Univ. of California, Berkeley, CA (United States); Tel Aviv Univ., Tel Aviv (Israel); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Kavli Energy NanoScience Inst., Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
- OSTI Identifier:
- 1564042
- Alternate Identifier(s):
- OSTI ID: 1527065
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 150; Journal Issue: 23; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Levy, Amikam, Dou, Wenjie, Rabani, Eran, and Limmer, David T. A complete quasiclassical map for the dynamics of interacting fermions. United States: N. p., 2019.
Web. doi:10.1063/1.5099987.
Levy, Amikam, Dou, Wenjie, Rabani, Eran, & Limmer, David T. A complete quasiclassical map for the dynamics of interacting fermions. United States. doi:https://doi.org/10.1063/1.5099987
Levy, Amikam, Dou, Wenjie, Rabani, Eran, and Limmer, David T. Wed .
"A complete quasiclassical map for the dynamics of interacting fermions". United States. doi:https://doi.org/10.1063/1.5099987. https://www.osti.gov/servlets/purl/1564042.
@article{osti_1564042,
title = {A complete quasiclassical map for the dynamics of interacting fermions},
author = {Levy, Amikam and Dou, Wenjie and Rabani, Eran and Limmer, David T.},
abstractNote = {We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. In conclusion, the numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.},
doi = {10.1063/1.5099987},
journal = {Journal of Chemical Physics},
number = 23,
volume = 150,
place = {United States},
year = {2019},
month = {6}
}
Web of Science
Works referenced in this record:
Quantum master equation for electron transport through quantum dots and single molecules
journal, December 2006
- Harbola, Upendra; Esposito, Massimiliano; Mukamel, Shaul
- Physical Review B, Vol. 74, Issue 23
A classical analog for electronic degrees of freedom in nonadiabatic collision processes
journal, April 1979
- Meyera), Hans‐Dieter; Miller, William H.
- The Journal of Chemical Physics, Vol. 70, Issue 7
A Cartesian classical second-quantized many-electron Hamiltonian, for use with the semiclassical initial value representation
journal, October 2012
- Li, Bin; Miller, William H.
- The Journal of Chemical Physics, Vol. 137, Issue 15
Nonequilibrium dynamics of the Anderson impurity model
journal, September 1998
- Hettler, Matthias H.; Kroha, Johann; Hershfield, Selman
- Physical Review B, Vol. 58, Issue 9
Importance sampling large deviations in nonequilibrium steady states. I
journal, March 2018
- Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.
- The Journal of Chemical Physics, Vol. 148, Issue 12
Kinetic equations for transport through single-molecule transistors
journal, December 2008
- Leijnse, M.; Wegewijs, M. R.
- Physical Review B, Vol. 78, Issue 23
Multiconfiguration time-dependent Hartree impurity solver for nonequilibrium dynamical mean-field theory
journal, January 2015
- Balzer, Karsten; Li, Zheng; Vendrell, Oriol
- Physical Review B, Vol. 91, Issue 4
Transport in molecular states language: Generalized quantum master equation approach
journal, May 2009
- Esposito, Massimiliano; Galperin, Michael
- Physical Review B, Vol. 79, Issue 20
Classical models for electronic degrees of freedom: The second‐quantized many‐electron Hamiltonian
journal, May 1986
- Miller, William H.; White, Kim A.
- The Journal of Chemical Physics, Vol. 84, Issue 9
A Cartesian quasi-classical model to nonequilibrium quantum transport: The Anderson impurity model
journal, March 2013
- Li, Bin; Levy, Tal J.; Swenson, David W. H.
- The Journal of Chemical Physics, Vol. 138, Issue 10
Classical trajectory model for electronically nonadiabatic collision phenomena. A classical analog for electronic degrees of freedom
journal, December 1978
- Miller, W. H.; McCurdy, C. W.
- The Journal of Chemical Physics, Vol. 69, Issue 11
Semiclassical representations of electronic structure and dynamics
journal, January 2004
- Van Voorhis, Troy; Reichman, David R.
- The Journal of Chemical Physics, Vol. 120, Issue 2
Real-Time Dynamics in Quantum-Impurity Systems: A Time-Dependent Numerical Renormalization-Group Approach
journal, October 2005
- Anders, Frithjof B.; Schiller, Avraham
- Physical Review Letters, Vol. 95, Issue 19
A semiclassical model for the non-equilibrium quantum transport of a many-electron Hamiltonian coupled to phonons
journal, May 2012
- Swenson, David W. H.; Cohen, Guy; Rabani, Eran
- Molecular Physics, Vol. 110, Issue 9-10
Including quantum effects in the dynamics of complex (i.e., large) molecular systems
journal, October 2006
- Miller, William H.
- The Journal of Chemical Physics, Vol. 125, Issue 13
Surface hopping with a manifold of electronic states. III. Transients, broadening, and the Marcus picture
journal, June 2015
- Dou, Wenjie; Nitzan, Abraham; Subotnik, Joseph E.
- The Journal of Chemical Physics, Vol. 142, Issue 23
Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems
journal, November 2016
- Schinabeck, C.; Erpenbeck, A.; Härtle, R.
- Physical Review B, Vol. 94, Issue 20
Phonon dynamics in correlated quantum systems driven away from equilibrium
journal, September 2014
- Wilner, Eli Y.; Wang, Haobin; Thoss, Michael
- Physical Review B, Vol. 90, Issue 11
Nonequilibrium electron transport using the density matrix renormalization group method
journal, September 2004
- Schmitteckert, Peter
- Physical Review B, Vol. 70, Issue 12
Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state
journal, May 2014
- Wilner, Eli Y.; Wang, Haobin; Thoss, Michael
- Physical Review B, Vol. 89, Issue 20
Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model
journal, September 2015
- Dorda, Antonius; Ganahl, Martin; Evertz, Hans Gerd
- Physical Review B, Vol. 92, Issue 12
Semiclassical Description of Nonadiabatic Quantum Dynamics
journal, January 1997
- Stock, Gerhard; Thoss, Michael
- Physical Review Letters, Vol. 78, Issue 4
On the exact continuous mapping of fermions
journal, August 2018
- Montoya-Castillo, Andrés; Markland, Thomas E.
- Scientific Reports, Vol. 8, Issue 1
Memory effects in nonequilibrium quantum impurity models
journal, August 2011
- Cohen, Guy; Rabani, Eran
- Physical Review B, Vol. 84, Issue 7
Nanoscale device modeling: the Green’s function method
journal, October 2000
- Datta, Supriyo
- Superlattices and Microstructures, Vol. 28, Issue 4
Bold-line diagrammatic Monte Carlo method: General formulation and application to expansion around the noncrossing approximation
journal, August 2010
- Gull, Emanuel; Reichman, David R.; Millis, Andrew J.
- Physical Review B, Vol. 82, Issue 7
Classical mapping for Hubbard operators: Application to the double-Anderson model
journal, May 2014
- Li, Bin; Miller, William H.; Levy, Tal J.
- The Journal of Chemical Physics, Vol. 140, Issue 20
Diagrammatic Monte Carlo simulation of nonequilibrium systems
journal, January 2009
- Werner, Philipp; Oka, Takashi; Millis, Andrew J.
- Physical Review B, Vol. 79, Issue 3
Taming the Dynamical Sign Problem in Real-Time Evolution of Quantum Many-Body Problems
journal, December 2015
- Cohen, Guy; Gull, Emanuel; Reichman, David R.
- Physical Review Letters, Vol. 115, Issue 26
Bistability in a nonequilibrium quantum system with electron-phonon interactions
journal, July 2013
- Wilner, Eli Y.; Wang, Haobin; Cohen, Guy
- Physical Review B, Vol. 88, Issue 4
Absence of Coulomb Blockade in the Anderson Impurity Model at the Symmetric Point
journal, May 2019
- Levy, Amikam; Kidon, Lyran; Bätge, Jakob
- The Journal of Physical Chemistry C, Vol. 123, Issue 22
Decoherence and lead-induced interdot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach
journal, December 2013
- Härtle, R.; Cohen, G.; Reichman, D. R.
- Physical Review B, Vol. 88, Issue 23
Real-time diagrammatic Monte Carlo for nonequilibrium quantum transport
journal, April 2009
- Schiró, Marco; Fabrizio, Michele
- Physical Review B, Vol. 79, Issue 15
Numerically exact path-integral simulation of nonequilibrium quantum transport and dissipation
journal, November 2010
- Segal, Dvira; Millis, Andrew J.; Reichman, David R.
- Physical Review B, Vol. 82, Issue 20
Molecular transport junctions: vibrational effects
journal, February 2007
- Galperin, Michael; Ratner, Mark A.; Nitzan, Abraham
- Journal of Physics: Condensed Matter, Vol. 19, Issue 10
First-principles based matrix Green's function approach to molecular electronic devices: general formalism
journal, August 2002
- Xue, Yongqiang; Datta, Supriyo; Ratner, Mark A.
- Chemical Physics, Vol. 281, Issue 2-3
A semiclasical justification for the use of non-spreading wavepackets in dynamics calculations
journal, November 1984
- Herman, Michael F.; Kluk, Edward
- Chemical Physics, Vol. 91, Issue 1
Self-Consistent Quantum Master Equation Approach to Molecular Transport
journal, July 2010
- Esposito, Massimiliano; Galperin, Michael
- The Journal of Physical Chemistry C, Vol. 114, Issue 48
A multilayer multiconfiguration time-dependent Hartree study of the nonequilibrium Anderson impurity model at zero temperature
journal, June 2018
- Wang, Haobin; Thoss, Michael
- Chemical Physics, Vol. 509
Numerical renormalization group method for quantum impurity systems
journal, April 2008
- Bulla, Ralf; Costi, Theo A.; Pruschke, Thomas
- Reviews of Modern Physics, Vol. 80, Issue 2
A unified ab initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures
journal, July 2017
- Cao, L.; Bolsinger, V.; Mistakidis, S. I.
- The Journal of Chemical Physics, Vol. 147, Issue 4
Semiclassical approach to dynamics of interacting fermions
journal, September 2017
- Davidson, Shainen M.; Sels, Dries; Polkovnikov, Anatoli
- Annals of Physics, Vol. 384
Application of a semiclassical model for the second-quantized many-electron Hamiltonian to nonequilibrium quantum transport: The resonant level model
journal, April 2011
- Swenson, David W. H.; Levy, Tal; Cohen, Guy
- The Journal of Chemical Physics, Vol. 134, Issue 16
Semiclassical propagation for multidimensional systems by an initial value method
journal, August 1994
- Kay, Kenneth G.
- The Journal of Chemical Physics, Vol. 101, Issue 3
Real-Time Path Integral Approach to Nonequilibrium Many-Body Quantum Systems
journal, May 2008
- Mühlbacher, Lothar; Rabani, Eran
- Physical Review Letters, Vol. 100, Issue 17
Born-Oppenheimer Dynamics, Electronic Friction, and the Inclusion of Electron-Electron Interactions
journal, July 2017
- Dou, Wenjie; Miao, Gaohan; Subotnik, Joseph E.
- Physical Review Letters, Vol. 119, Issue 4
Localized Magnetic States in Metals
journal, October 1961
- Anderson, P. W.
- Physical Review, Vol. 124, Issue 1
A simple kinetic equation for steady-state quantum transport
journal, October 1990
- Datta, S.
- Journal of Physics: Condensed Matter, Vol. 2, Issue 40
Iterative real-time path integral approach to nonequilibrium quantum transport
journal, May 2008
- Weiss, S.; Eckel, J.; Thorwart, M.
- Physical Review B, Vol. 77, Issue 19
Works referencing / citing this record:
Special topic on dynamics of open quantum systems
journal, January 2020
- Berkelbach, Timothy C.; Thoss, Michael
- The Journal of Chemical Physics, Vol. 152, Issue 2