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

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.

21 pages, 8 figures

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• Quantum Mpemba effect without global symmetries
• Tuning the Quantum Mpemba Effect in Isolated System by Initial State Engineering
• Speeding up Pontus-Mpemba effects via dynamical phase transitions
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Quantum Mpemba effect in parity-time symmetric systems
• Quantum Mpemba effect in chaotic systems with conservation laws