Two-Time Correlation Functions in Dissipative and Interacting Bose-Hubbard Chains

TL;DR

This paper introduces a systematic method to derive and solve hierarchies of equations for two-time correlation functions in open many-body quantum systems, enabling analysis of their full temporal evolution.

Contribution

It presents a novel approach for deriving and closing equations for two-time correlations in open quantum systems, extending beyond stationary states.

Findings

Applicable to dissipative Bose-Hubbard chains

Allows analysis of full temporal evolution

Demonstrated on spectral weight functions

Abstract

A method is presented for the systematic derivation of a hierarchy of coupled equations for the computation of two-time correlation functions of operators for open many-body quantum systems. We show how these systems of equations can be closed in mean-field and beyond approximations. Results for the specific example of the spectral weight functions are discussed. Our method allows one to access the full temporal evolution, not just the stationary solution, of non-equilibrium open quantum problems described by a Markovian master equation.