Lindblad master equation approach to superconductivity in open quantum systems

TL;DR

This paper develops a Lindblad master equation framework to analyze superconductivity in open quantum Fermi-systems, focusing on fixed points and stability of the order parameter.

Contribution

It introduces a novel approach using Lindblad equations to study superconductivity in open quantum systems with pairing interactions.

Findings

Fixed points of the covariance matrix are identified.

Stability analysis of the order parameter is performed.

The dynamics of quasiparticle exchange with the bath is characterized.

Abstract

We consider an open quantum Fermi-system which consists of a single degenerate level with pairing interactions embedded into a superconducting bath. The time evolution of the reduced density matrix for the system is given by Linblad master equation, where the dissipators describe exchange of Bogoliubov quasiparticles with the bath. We obtain fixed points of the time evolution equation for the covariance matrix and study their stability by analyzing full dynamics of the order parameter.