Real-time broadening of bath-induced density profiles from closed-system correlation functions

TL;DR

This paper links the dynamics of open quantum spin chains under Lindblad dissipation to closed-system correlation functions, revealing how transport properties like diffusion emerge from intrinsic correlations.

Contribution

It demonstrates that, for weak driving, open-system dynamics can be reconstructed from closed-system correlation functions, bridging Lindblad and linear response approaches.

Findings

Closed and open system transport properties agree for weak driving.

Superdiffusive and diffusive scaling observed in different regimes.

Numerical validation on the spin-1/2 XXZ chain.

Abstract

The Lindblad master equation is one of the main approaches to open quantum systems. While it has been widely applied in the context of condensed matter systems to study properties of steady states in the limit of long times, the actual route to such steady states has attracted less attention yet. Here, we investigate the nonequilibrium dynamics of spin chains with a local coupling to a single Lindblad bath and analyze the transport properties of the induced magnetization. Combining typicality and equilibration arguments with stochastic unraveling, we unveil for the case of weak driving that the dynamics in the open system can be constructed on the basis of correlation functions in the closed system, which establishes a connection between the Lindblad approach and linear response theory at finite times. In this way, we provide a particular example where closed and open approaches to quantum transport agree strictly. We demonstrate this fact numerically for the spin-1/2 XXZ chain at the isotropic point and in the easy-axis regime, where superdiffusive and diffusive scaling is observed, respectively.