Green's function approach to Josephson dot dynamics and application to quantum Mpemba effects

We develop a Green's function approach for the nonequilibrium dynamics of multilevel 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 Coulomb interactions can also 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 single-channel junction, we show that both types of quantum Mpemba effects allowed in open quantum systems can occur. We also study an intermediate-length junction, where spin-orbit interactions and a Zeeman field are included. Again quantum Mpemba effects are predicted.