Green's Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects

TL;DR

This paper introduces a simplified Green's function method to analyze the nonequilibrium dynamics of quantum dots in Josephson junctions, revealing the possibility of quantum Mpemba effects after rapid phase quenches.

Contribution

A new Green's function approach that simplifies the analysis of quantum dot Josephson junctions and demonstrates quantum Mpemba effects under various conditions.

Findings

Quantum Mpemba effects occur in short single-channel junctions.

Quantum Mpemba effects are also predicted in intermediate-length junctions with spin-orbit and Zeeman interactions.

The method extends analysis capabilities beyond traditional scattering state approaches.

Abstract

We develop a Green's function approach for the nonequilibrium dynamics of multi-level quantum dots coupled to multiple fermionic reservoirs in the presence of a bosonic environment. Our theory is simpler than the Keldysh approach and goes beyond scattering state constructions. In concrete terms, we study Josephson junctions containing a quantum dot and coupled to an electromagnetic environment. In the dot region, spin-orbit interactions, a Zeeman field, and in principle also Coulomb interactions can be included. We then study quantum Mpemba effects, assuming that the average phase difference across the Josephson junction is subject to a rapid quench. For a short singlechannel junction, we show that both types of quantum Mpemba effects allowed in open quantum systems are possible. We also study an intermediate-length junction, where spin-orbit interactions and a Zeeman field are included. Again quantum Mpemba effects are predicted.