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Title: Reduced Dynamics with Initial Correlations, and Time-Dependent Environment and Hamiltonians

Abstract

We consider a small system {ital s} in a bath {ital b}, in the case that the state of {ital b} and all Hamiltonians are possibly time dependent. We obtain for the reduced density matrix of {ital s} and exact evolution equation {rho}{sub {ital s}}({ital t})={Lambda}({ital t},{tau}){rho}{sub {ital s}}({tau}), with ({partial_derivative}/{partial_derivative}{ital t}){Lambda}({ital t},{tau})={Gamma}({ital t},{tau}){Lambda}({ital t},{tau}), where {Gamma}({ital t},{tau}) depends on the system-bath correlations at time {tau}. The open evolutor {Lambda}({ital t},{tau}) can (but need not) be chosen completely positive. It is argued that as {ital t}{minus}{tau} increases, {Gamma}({ital t},{tau}){r_arrow}{Gamma}{sub 0}({ital t}) forgets the initial correlations and tends to Lindblad form in time-coarse-grained weak coupling limits. {copyright} {ital 1996 The American Physical Society.}

Authors:
 [1]
  1. Departement de Genie Physique, Ecole Polytechnique, Montreal, Quebec, H3C 3A7 (CANADA)
Publication Date:
OSTI Identifier:
388376
Resource Type:
Journal Article
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 77; Journal Issue: 16; Other Information: PBD: Oct 1996
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; HAMILTONIANS; TIME DEPENDENCE; CORRELATIONS; DENSITY MATRIX; COUPLING; FLUCTUATIONS; MAGNETIC RESONANCE; PROJECTION OPERATORS

Citation Formats

Royer, A. Reduced Dynamics with Initial Correlations, and Time-Dependent Environment and Hamiltonians. United States: N. p., 1996. Web. doi:10.1103/PhysRevLett.77.3272.
Royer, A. Reduced Dynamics with Initial Correlations, and Time-Dependent Environment and Hamiltonians. United States. doi:10.1103/PhysRevLett.77.3272.
Royer, A. Tue . "Reduced Dynamics with Initial Correlations, and Time-Dependent Environment and Hamiltonians". United States. doi:10.1103/PhysRevLett.77.3272.
@article{osti_388376,
title = {Reduced Dynamics with Initial Correlations, and Time-Dependent Environment and Hamiltonians},
author = {Royer, A},
abstractNote = {We consider a small system {ital s} in a bath {ital b}, in the case that the state of {ital b} and all Hamiltonians are possibly time dependent. We obtain for the reduced density matrix of {ital s} and exact evolution equation {rho}{sub {ital s}}({ital t})={Lambda}({ital t},{tau}){rho}{sub {ital s}}({tau}), with ({partial_derivative}/{partial_derivative}{ital t}){Lambda}({ital t},{tau})={Gamma}({ital t},{tau}){Lambda}({ital t},{tau}), where {Gamma}({ital t},{tau}) depends on the system-bath correlations at time {tau}. The open evolutor {Lambda}({ital t},{tau}) can (but need not) be chosen completely positive. It is argued that as {ital t}{minus}{tau} increases, {Gamma}({ital t},{tau}){r_arrow}{Gamma}{sub 0}({ital t}) forgets the initial correlations and tends to Lindblad form in time-coarse-grained weak coupling limits. {copyright} {ital 1996 The American Physical Society.}},
doi = {10.1103/PhysRevLett.77.3272},
journal = {Physical Review Letters},
number = 16,
volume = 77,
place = {United States},
year = {1996},
month = {10}
}