Quantum correlation functions and the classical limit

TL;DR

This paper explores how quantum systems transition to classical behavior by linking quantum correlation functions with classical stochastic processes, providing a formal framework applicable to various quantum systems.

Contribution

It establishes a formal connection between the CTP generating functional and the decoherence functional, enabling explicit derivation of classical stochastic processes from quantum descriptions.

Findings

Explicit construction of classical stochastic processes from quantum correlation functions.

Simplified results for Gaussian quantum processes.

Application to quantum Brownian motion and quantum fields in curved spacetime.

Abstract

We study the transition from the full quantum mechanical description of physical systems to an approximate classical stochastic one. Our main tool is the identification of the closed-time-path (CTP) generating functional of Schwinger and Keldysh with the decoherence functional of the consistent histories approach. Given a degree of coarse-graining in which interferences are negligible, we can explicitly write a generating functional for the effective stochastic process in terms of the CTP generating functional. This construction gives particularly simple results for Gaussian processes. The formalism is applied to simple quantum systems, quantum Brownian motion, quantum fields in curved spacetime. Perturbation theory is also explained. We conclude with a discussion on the problem of backreaction of quantum fields in spacetime geometry.