From Feynman-Vernon to Wiener Stochastic Path Integral

TL;DR

This paper bridges quantum and classical stochastic dynamics by deriving a Wiener path integral from the Feynman-Vernon formalism, enabling a classical interpretation of quantum open systems and addressing the inverse problem of influence functional construction.

Contribution

It establishes a direct link between quantum Feynman-Vernon and classical Wiener path integrals, providing a new framework for analyzing open quantum systems in the strong decoherence limit.

Findings

Quantum Feynman measure transforms into Wiener measure.

System dynamics can be represented as a stochastic process in the Wigner function framework.

Inverse construction of quantum influence functional from classical Langevin equations is demonstrated.

Abstract

We establish a direct connection between the Feynman-Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics. By considering a generalized influence functional in the strong decoherence limit, we demonstrate that integrating over the quantum coherence length leads to a derivation of stochastic Langevin dynamics. Specifically, we show that the quantum Feynman measure transforms into the stochastic Wiener measure. Applying this framework to the Wigner function representation, we show that the system follows a stochastic path interpretable via classical probability theory. Finally, we address the inverse problem: constructing an equivalent quantum influence functional from a given classical Langevin equation.