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physica status solidi (b)

Stochastic and numerical approaches to dissipative quantum dynamics: path integrals and beyond

Jürgen T. Stockburger

Published Apr 24, 2003• 9 citations
Publisher

Abstract

Abstract Recent advances using non‐Markovian stochastic techniques in the treatment of system–reservoir models of quantum dissipation are reviewed, outlining their derivation from the influence functional formalism and discussing their new features and potential applications. A coherent perspective of the salient features in the mathematical foundations of dissipative quantum mechanics, diverse established perturbative and numerical methods, and more recent non‐Markovian stochastic approaches is attempted.

DOI
10.1002/pssb.200301796

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Abstract Recent advances using non‐Markovian stochastic techniques in the treatment of system–reservoir models of quantum dissipation are reviewed, outlining their derivation from the influence functional formalism and discussing their new features and potential applications. A coherent perspective of the salient features in the mathematical foundations of dissipative quantum mechanics, diverse established perturbative and numerical methods, and more recent non‐Markovian stochastic approaches is attempted.
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We consider the non-Markovian Langevin evolution of a dissipative dynamical system in quantum mechanics in the path integral formalism. After discussing the role of the frequency cutoff for the interaction of the system with the heat bath and the kernel and noise correlator that follow from the most common choices, we derive an analytic expansion for the exact non-Markovian dissipation kernel and the corresponding colored noise in the general case that is consistent with the fluctuation-dissipation theorem and incorporates systematically non-local corrections. We illustrate the modifications to results obtained using the traditional (Markovian) Langevin approach in the case of the exponential kernel and analyze the case of the non-Markovian Brownian motion.
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