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Title: 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:
ORCiD logo [1]; ORCiD logo [2];  [3]; ORCiD logo [4]
+ Show Author Affiliations
  1. Univ. of California, Berkeley, CA (United States); Tel Aviv Univ., Tel Aviv (Israel)
  2. Univ. of California, Berkeley, CA (United States)
  3. Univ. of California, Berkeley, CA (United States); Tel Aviv Univ., Tel Aviv (Israel); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  4. 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.
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Levy, Amikam, Dou, Wenjie, Rabani, Eran, & Limmer, David T. A complete quasiclassical map for the dynamics of interacting fermions. United States. https://doi.org/10.1063/1.5099987
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Levy, Amikam, Dou, Wenjie, Rabani, Eran, and Limmer, David T. Wed . "A complete quasiclassical map for the dynamics of interacting fermions". United States. https://doi.org/10.1063/1.5099987. https://www.osti.gov/servlets/purl/1564042.
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@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}
}
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https://doi.org/10.1063/1.5099987
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Works referenced in this record:

Quantum master equation for electron transport through quantum dots and single molecules
journal, December 2006

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
  • DOI: 10.1063/1.437910

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
  • DOI: 10.1063/1.4757935

Nonequilibrium dynamics of the Anderson impurity model
journal, September 1998

  • Hettler, Matthias H.; Kroha, Johann; Hershfield, Selman
  • Physical Review B, Vol. 58, Issue 9
  • DOI: 10.1103/physrevb.58.5649

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
  • DOI: 10.1063/1.5003151

Kinetic equations for transport through single-molecule transistors
journal, December 2008

Multiconfiguration time-dependent Hartree impurity solver for nonequilibrium dynamical mean-field theory
journal, January 2015

Transport in molecular states language: Generalized quantum master equation approach
journal, May 2009

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
  • DOI: 10.1063/1.450655

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
  • DOI: 10.1063/1.4793747

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
  • DOI: 10.1063/1.436463

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
  • DOI: 10.1063/1.1630963

Real-Time Dynamics in Quantum-Impurity Systems: A Time-Dependent Numerical Renormalization-Group Approach
journal, October 2005

A semiclassical model for the non-equilibrium quantum transport of a many-electron Hamiltonian coupled to phonons
journal, May 2012

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
  • DOI: 10.1063/1.2211608

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
  • DOI: 10.1063/1.4922513

Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems
journal, November 2016

Phonon dynamics in correlated quantum systems driven away from equilibrium
journal, September 2014

Nonequilibrium electron transport using the density matrix renormalization group method
journal, September 2004

Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state
journal, May 2014

Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model
journal, September 2015

Semiclassical Description of Nonadiabatic Quantum Dynamics
journal, January 1997

On the exact continuous mapping of fermions
journal, August 2018

Memory effects in nonequilibrium quantum impurity models
journal, August 2011

Nanoscale device modeling: the Green’s function method
journal, October 2000

Bold-line diagrammatic Monte Carlo method: General formulation and application to expansion around the noncrossing approximation
journal, August 2010

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
  • DOI: 10.1063/1.4878736

Diagrammatic Monte Carlo simulation of nonequilibrium systems
journal, January 2009

Taming the Dynamical Sign Problem in Real-Time Evolution of Quantum Many-Body Problems
journal, December 2015

Bistability in a nonequilibrium quantum system with electron-phonon interactions
journal, July 2013

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
  • DOI: 10.1021/acs.jpcc.9b04132

Real-time diagrammatic Monte Carlo for nonequilibrium quantum transport
journal, April 2009

Numerically exact path-integral simulation of nonequilibrium quantum transport and dissipation
journal, November 2010

Molecular transport junctions: vibrational effects
journal, February 2007

First-principles based matrix Green's function approach to molecular electronic devices: general formalism
journal, August 2002

A semiclasical justification for the use of non-spreading wavepackets in dynamics calculations
journal, November 1984

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
  • DOI: 10.1021/jp103369s

Numerical renormalization group method for quantum impurity systems
journal, April 2008

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
  • DOI: 10.1063/1.4993512

Semiclassical approach to dynamics of interacting fermions
journal, September 2017

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
  • DOI: 10.1063/1.3583366

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
  • DOI: 10.1063/1.467665

Real-Time Path Integral Approach to Nonequilibrium Many-Body Quantum Systems
journal, May 2008

Born-Oppenheimer Dynamics, Electronic Friction, and the Inclusion of Electron-Electron Interactions
journal, July 2017

Localized Magnetic States in Metals
journal, October 1961

A simple kinetic equation for steady-state quantum transport
journal, October 1990

Iterative real-time path integral approach to nonequilibrium quantum transport
journal, May 2008

Real-time path integral approach to nonequilibrium many-body quantum system
text, January 2007

Kinetic Equations for Transport Through Single-Molecule Transistors
text, January 2008

Transport in molecular states language: Generalized quantum master equation approach
text, January 2008

Numerically exact path integral simulation of nonequilibrium quantum transport and dissipation
text, January 2010

Memory Effects In Nonequilibrium Quantum Impurity Models
text, January 2011

Phonon dynamics in correlated quantum systems driven away from equilibrium
text, January 2014

Semiclassical approach to Dynamics of Interacting Fermions
text, January 2016

Importance sampling large deviations in nonequilibrium steady states. I
text, January 2017

Absence of Coulomb Blockade in the Anderson Impurity Model at the Symmetric Point
text, January 2019

Molecular Transport Junctions: Vibrational Effects
text, January 2006

The numerical renormalization group method for quantum impurity systems
text, January 2007

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