Non-perturbative treatment of open-system multi-time expectation values in Gaussian bosonic environments

TL;DR

This paper establishes conditions under which multi-time expectation values in open quantum systems interacting with Gaussian bosonic environments can be equivalently computed, enabling non-perturbative analysis of such systems.

Contribution

It proves the equivalence of multi-time expectation values for certain Gaussian bosonic environments and introduces a non-perturbative method for their evaluation.

Findings

Conditions for environment equivalence established

Non-perturbative evaluation method developed

Applicable to systems with continuous bosonic modes

Abstract

We determine the conditions for the equivalence between the multi-time expectation values of a general finite-dimensional open quantum system when interacting with, respectively, an environment undergoing a free unitary evolution or a discrete environment under a free evolution fixed by a proper Gorini-Kossakowski-Lindblad-Sudarshan generator. We prove that the equivalence holds if both environments are bosonic and Gaussian and if the one- and two-time correlation functions of the corresponding interaction operators are the same at all times. This result leads to a non-perturbative evaluation of the multi-time expectation values of operators and maps of open quantum systems interacting with a continuous set of bosonic modes by means of a limited number of damped modes, thus setting the ground for the investigation of open-system multi-time quantities in fully general regimes.