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Title: Generalized quantum master equations in and out of equilibrium: When can one win?

Abstract

Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights asmore » to when proceeding via the GQME approach can be used to improve the accuracy of simulations.« less

Authors:
 [1]; ORCiD logo [2];  [3];  [1]
+ Show Author Affiliations
  1. Stanford Univ., CA (United States). Dept. of Chemistry
  2. Columbia Univ., New York, NY (United States). Dept. of Chemistry
  3. Rutgers Univ., Piscataway, NJ (United States). Dept. of Chemistry and Chemical Biology
Publication Date:
Research Org.:
Univ. of California, Merced, CA (United States); Stanford Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
OSTI Identifier:
1471071
Alternate Identifier(s):
OSTI ID: 1252334; OSTI ID: 1526761
Grant/Contract Number:  
SC0014437
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 144; Journal Issue: 18; 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; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Kelly, Aaron, Montoya-Castillo, Andrés, Wang, Lu, and Markland, Thomas E. Generalized quantum master equations in and out of equilibrium: When can one win?. United States: N. p., 2016. Web. doi:10.1063/1.4948612.
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Kelly, Aaron, Montoya-Castillo, Andrés, Wang, Lu, & Markland, Thomas E. Generalized quantum master equations in and out of equilibrium: When can one win?. United States. https://doi.org/10.1063/1.4948612
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Kelly, Aaron, Montoya-Castillo, Andrés, Wang, Lu, and Markland, Thomas E. Tue . "Generalized quantum master equations in and out of equilibrium: When can one win?". United States. https://doi.org/10.1063/1.4948612. https://www.osti.gov/servlets/purl/1471071.
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@article{osti_1471071,
title = {Generalized quantum master equations in and out of equilibrium: When can one win?},
author = {Kelly, Aaron and Montoya-Castillo, Andrés and Wang, Lu and Markland, Thomas E.},
abstractNote = {Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.},
doi = {10.1063/1.4948612},
journal = {Journal of Chemical Physics},
number = 18,
volume = 144,
place = {United States},
year = {Tue May 10 00:00:00 EDT 2016},
month = {Tue May 10 00:00:00 EDT 2016}
}
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