On the Stochastic Limit of Quantum Field Theory

TL;DR

This paper rigorously derives the stochastic limit of a quantum system coupled to a Bose reservoir, resulting in master and Langevin equations, and applies it to atomic-electromagnetic interactions without common approximations.

Contribution

It provides a mathematically rigorous derivation of the stochastic limit in quantum field theory, extending previous heuristic approaches and applying it to realistic atomic interactions.

Findings

Derived the limiting evolution unitary for quantum systems with Bose reservoirs.

Obtained master and Langevin equations from the stochastic limit.

Applied results to atomic systems interacting with electromagnetic fields without simplifying approximations.

Abstract

The weak coupling limit for a quantum system, with discrete energy spectrum, coupled to a Bose reservoir with the most general linear interaction is considered: under this limit we have a quantum noise processes substituting for the field. We obtain a limiting evolution unitary on the system and noise space which, when reduced to the system's degrees of freedom, provide the master and Langevin equations that are postulated on heuristic grounds by physicists. In addition we give a concrete application of our results by deriving the evolution of an atomic system interacting with the electrodynamic field without recourse to either rotating wave or dipole approximations.