Exact c-number Representation of Non-Markovian Quantum Dissipation

TL;DR

This paper presents an exact stochastic Schr{"o}dinger equation representation for non-Markovian quantum dissipation, capturing memory effects and generalizing quantum state diffusion beyond the Markov approximation.

Contribution

It introduces a precise c-number stochastic framework for non-Markovian quantum dynamics, applicable at any temperature and damping strength, with explicit connection to classical Langevin equations.

Findings

Exact non-Markovian dynamics derived

Classical limit reduces to generalized Langevin equation

Application demonstrated on dissipative two-state system

Abstract

The reduced dynamics of a quantum system interacting with a linear heat bath finds an exact representation in terms of a stochastic Schr{\"o}dinger equation. All memory effects of the reservoir are transformed into noise correlations and mean-field friction. The classical limit of the resulting stochastic dynamics is shown to be a generalized Langevin equation, and conventional quantum state diffusion is recovered in the Born--Markov approximation. The non-Markovian exact dynamics, valid at arbitrary temperature and damping strength, is exemplified by an application to the dissipative two-state system.