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Title: Resummed memory kernels in generalized system-bath master equations

Abstract

Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate andmore » the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.« less

Authors:
Publication Date:
OSTI Identifier:
22419986
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 141; Journal Issue: 5; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOSONS; CONVERGENCE; EQUATIONS; HAMILTONIANS; KERNELS; POPULATION DYNAMICS; SPECTRAL DENSITY; SPIN; TIME DEPENDENCE

Citation Formats

Mavros, Michael G., and Van Voorhis, Troy, E-mail: tvan@mit.edu. Resummed memory kernels in generalized system-bath master equations. United States: N. p., 2014. Web. doi:10.1063/1.4891669.
Mavros, Michael G., & Van Voorhis, Troy, E-mail: tvan@mit.edu. Resummed memory kernels in generalized system-bath master equations. United States. https://doi.org/10.1063/1.4891669
Mavros, Michael G., and Van Voorhis, Troy, E-mail: tvan@mit.edu. 2014. "Resummed memory kernels in generalized system-bath master equations". United States. https://doi.org/10.1063/1.4891669.
@article{osti_22419986,
title = {Resummed memory kernels in generalized system-bath master equations},
author = {Mavros, Michael G. and Van Voorhis, Troy, E-mail: tvan@mit.edu},
abstractNote = {Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.},
doi = {10.1063/1.4891669},
url = {https://www.osti.gov/biblio/22419986}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 5,
volume = 141,
place = {United States},
year = {Thu Aug 07 00:00:00 EDT 2014},
month = {Thu Aug 07 00:00:00 EDT 2014}
}