Non-perturbative treatment of non-Markovian dynamics of open quantum systems

TL;DR

This paper establishes conditions under which the dynamics of open quantum systems interacting with different types of environments are equivalent, enabling more efficient non-perturbative analysis of complex non-Markovian behaviors.

Contribution

It proves the equivalence of dynamics for continuous and discrete bosonic environments under certain conditions, generalizing the pseudomodes approach for non-Markovian systems.

Findings

Equivalence of reduced dynamics for different environment types under specific conditions.

Efficient non-perturbative description of complex non-Markovian dynamics.

Generalization of the pseudomodes approach to broader scenarios.

Abstract

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments - one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (non-unitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, non-perturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open system dynamics.