Non-Markovian expansion in quantum dissipative systems

TL;DR

This paper develops an analytic expansion for non-Markovian quantum dissipation kernels and colored noise, improving the understanding of non-local effects in quantum Langevin dynamics.

Contribution

It introduces a systematic non-Markovian expansion for dissipation and noise kernels in quantum systems, consistent with fluctuation-dissipation theorem.

Findings

Derived an analytic expansion for non-Markovian kernels

Showed modifications to Markovian Langevin results with exponential kernels

Analyzed non-Markovian Brownian motion effects

Abstract

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.