Dissipative flow equations

TL;DR

This paper extends flow equation methods to open quantum systems described by Lindblad equations, enabling diagonalization of non-Hermitian operators and analyzing complex dissipative dynamics.

Contribution

It introduces three new generators for dissipative flow equations and demonstrates their effectiveness on single and multiple fermionic modes.

Findings

Successfully diagonalized Lindblad operators in various systems

Revealed interplay between coherent dynamics and localized losses

Applicable to non-Hermitian Hamiltonians

Abstract

We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We introduce and discuss three different generators of the flow that transform a linear non-Hermitian operator into a diagonal one. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode. We then move to problems with many fermionic modes and discuss the interplay between coherent (disordered) dynamics and localized losses. Our method can also be applied to non-Hermitian Hamiltonians.