Long-range Kitaev chain in a thermal bath: Analytic techniques for time-dependent systems and environments

TL;DR

This paper develops an analytical framework for studying the nonequilibrium dynamics of open quantum systems, specifically a Kitaev chain coupled to baths, under time-dependent conditions, enabling insights into thermalization, dissipation, and driven quantum phenomena.

Contribution

It introduces a minimal, analytically solvable model for open quantum systems with time-dependent parameters, combining Lindblad dynamics and Third Quantization techniques.

Findings

Analytic solutions for the correlation matrix evolution.

Efficient numerical descriptions of driven open Kitaev chains.

Insights into the interplay of dissipation and nonadiabatic excitations.

Abstract

We construct and solve a "minimal model" with which nonequilibrium phenomena in many-body open quantum systems can be studied analytically under time-dependent parameter changes in the system and/or the bath. Coupling a suitable configuration of baths to a Kitaev chain, we self-consistently derive a Lindblad master equation which, at least in the absence of explicit time dependencies, leads to thermalization. Using the method of Third Quantization we derive time-evolution equations for the correlation matrix, which we relate to the occupation of the system's quasiparticle modes. These results permit analytic and efficient numeric descriptions of the nonequilibrium dynamics of open Kitaev chains under a wide range of driving protocols, which in turn facilitate the investigation of the interplay between bath-induced dissipation and the generation of coherent excitations by nonadiabatic driving. We advertise this minimal model of maximum simplicity for the study of finite-temperature generalizations of Kibble-Zurek ramps, Floquet physics, and many other nonequilibrium protocols of quantum many-body systems driven by time-varying parameters and/or temperatures.