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arXiv:2501.11609 · Physical review. B./Physical review. B

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

Kateryna Zatsarynna, Andrea Kazemi Nava, Reinhold Egger, Alex Zazunov

Published Mar 17, 2025• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.111.104506

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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.
The Mpemba effect has initially been noticed in macroscopic systems-namely that hot water can freeze faster than cold water-but recently its extension to open quantum systems has attracted significant attention. This phenomenon can be explained in the context of nonequilibrium thermodynamics of Markovian systems, relying on the amplitudes of different decay modes of the system dynamics. Here, we study the Mpemba effect in a single-level quantum dot coupled to a thermal bath, highlighting the role of the sign and magnitude of the electron-electron interaction in the occurrence of the Mpemba effect. We gain physical insights into the decay modes from a dissipative symmetry of this system called fermionic duality. Based on this analysis of the relaxation to equilibrium of the dot, we derive criteria for the occurrence of the Mpemba effect using two thermodynamically relevant measures of the distance to equilibrium, the nonequilibrium free energy and the dot energy. We furthermore compare this effect to a possible exponential speedup of the relaxation. Finally, we propose experimentally relevant schemes for the state preparation and explore different ways of observing the Mpemba effect in quantum dots in experiments.
Abstract Harnessing non-Markovian effects has emerged as a resource for quantum control, where a structured environment can act as a quantum memory. We investigate the quench dynamics from specific initial states to equilibrium steady states in strongly correlated quantum dot systems. The distance between quantum states is quantified using the Bures metric, which endows the space of reduced density matrices with a Riemannian geometric structure. Using the numerically exact hierarchical equations of motion method, we demonstrate a quantum Mpemba effect (QME) arising from non-Markovianity. Unlike previous studies centered on non-interacting limits, we reveal a distinct non-Markovian QME uniquely driven by the initial-state-dependent formation of the many-body Kondo resonance. Furthermore, by tracking the dynamical evolution in the generalized Bloch parameter space, we uncover an intrinsic QME. This trajectory-dependent analysis provides a rigorous geometric perspective on the circuitous relaxation pathways driven by Kondo correlations. Our results underscore the critical role of memory effects in quantum quench dynamics and suggest new pathways for controlling anomalous relaxation in open quantum systems.
We consider a finite quantum system under slow driving and weakly coupled to thermal reservoirs at different temperatures. We present a systematic derivation of the quantum master equation for the density matrix and the out-of-time-order correlators. We start from the microscopic Hamiltonian and we formulate the equations ruling the dynamics of these quantities by recourse to the Schwinger-Keldysh nonequilibrium Green's function formalism, performing a perturbative expansion in the coupling between the system and the reservoirs. We focus on the adiabatic dynamics, which corresponds to considering the linear response in the ratio between the relaxation time due to the system-reservoir coupling and the time scale associated to the driving. We calculate the particle and energy fluxes. We illustrate the formalism in the case of a qutrit coupled to bosonic reservoirs and of a pair of interacting quantum dots attached to fermionic reservoirs, also discussing the relevance of coherent effects.
We develop a low-energy nonequilibrium field theory for weakly interacting quantum dots. The theory is based on the Keldysh field integral in the spin channel of the quantum dot described by the single-impurity Anderson Hamiltonian. The effective Keldysh action is a functional of the Hubbard-Stratonovich magnetization field decoupling the quantum dot spin channel. We expand this action up to the second order with respect to the magnetization field, which allows one to describe nonequilibrium interacting quantum dots at low temperatures and weak electron-electron interactions, up to the contacts-dot coupling energy. Besides its simplicity, an additional advantage of the theory is that it correctly describes the unitary limit, giving the correct result for the conductance maximum. Thus our theory establishes an alternative simple method relevant for investigation of weakly interacting nonequilibrium nanodevices.
We generalize the classical thermal Mpemba effect (where an initially hot system relaxes faster to the final equilibrium state than a cold one) to open quantum systems coupled to several reservoirs. We show that, in general, two different types of quantum Mpemba effects are possible. They may be distinguished by quantum state tomography. However, the existence of a quantum Mpemba effect (without determining the type) can already be established by measuring simpler observables such as currents or energies. We illustrate our general results for the experimentally feasible case of an interacting two-site Kitaev model coupled to two metallic leads.
We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold) cross each other at finite time (and thereby reverse their identities; i.e., hot becomes cold and vice versa) to generate thermal quantum Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.