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 onebody operators. In order to accommodate the effect of twobody terms, we further impose quantization on the spindependent occupation numbers in the classical equations of motion, with a parameter that is determined selfconsistently. 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 Laboratory (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22). Materials Sciences & Engineering Division; USDOE
 OSTI Identifier:
 1564042
 Alternate Identifier(s):
 OSTI ID: 1527065
 Grant/Contract Number:
 AC0205CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 150; Journal Issue: 23; Journal ID: ISSN 00219606
 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. 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. 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 onebody operators. In order to accommodate the effect of twobody terms, we further impose quantization on the spindependent occupation numbers in the classical equations of motion, with a parameter that is determined selfconsistently. 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
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Works referencing / citing this record:
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