Lindblad master equation approach to the dissipative quench dynamics of planar superconductors

TL;DR

This paper uses the Lindblad master equation to analyze the nonequilibrium dynamics of open 2D superconductors after a Hamiltonian quench, revealing how dissipation stabilizes the system and induces a dynamical phase transition.

Contribution

It introduces a novel application of the Lindblad approach to characterize dynamical phase transitions in open superconducting systems post-quench.

Findings

Dissipation acts as an effective stabilization mechanism.

A dynamical phase transition occurs due to phase mismatch.

The method characterizes the transition via superconducting gap and fidelity.

Abstract

We employ the Lindblad master equation method to study the nonequilibrium dynamics following a parametric quench in the Hamiltonian of an open, two-dimensional superconducting system coupled to an external bath. Within our approach we show how, in the open system, the dissipation works as an effective stabilization mechanism in the time evolution of the system after the quench. Eventually, we evidence how the mismatch between the phases corresponding to the initial and to the final state of the system determines a dynamical phase transition between the two distinct phases. Our method allows for fully characterizing the dynamical phase transition in an open system in several cases of physical relevance, by means of a combined study of the time-dependent superconducting gap and of the fidelity between density matrices.