Adiabatic response for Lindblad dynamics

TL;DR

This paper investigates the adiabatic response of open quantum systems described by Lindblad dynamics, revealing that transport coefficients are governed by parallel transport and adiabatic curvature, especially when stationary states are projections.

Contribution

It provides explicit formulas for transport coefficients in Lindblad systems and clarifies the role of adiabatic curvature when stationary states are projections.

Findings

Transport coefficients are governed by parallel transport on the manifold of stationary states.

Response coefficients for systems with projection stationary states are given by the adiabatic curvature.

Formulas for fluxes in Lindblad dynamics are simplified and explicit.

Abstract

We study the adiabatic response of open systems governed by Lindblad evolutions. In such systems, there is an ambiguity in the assignment of observables to fluxes (rates) such as velocities and currents. For the appropriate notion of flux, the formulas for the transport coefficients are simple and explicit and are governed by the parallel transport on the manifold of instantaneous stationary states. Among our results we show that the response coefficients of open systems, whose stationary states are projections, is given by the adiabatic curvature.