A closed system setting for quantum thermalisation in free fermions

Abstract:We study thermalisation and the possible occurrence of the Mpemba effect in a closed quantum setting that mimics the interaction of a system with thermal reservoirs coupled only at its boundaries. Specifically, we consider a tripartite geometry in which a finite chain, initially prepared at a finite temperature, is suddenly connected on both sides to two semi-infinite chains of the same nature held at a different temperature. These outer chains act as thermal baths, while the full system evolves unitarily under a homogeneous Hamiltonian. This setup provides a simple quantum realisation of a temperature quench and closely resembles the original scenario in which the classical Mpemba effect was first observed. We focus on two paradigmatic free-fermion models, the XX chain and the transverse-field Ising chain, which respectively preserve and break the global $U(1)$ particle-number symmetry. As a probe of relaxation, we consider the Frobenius distance between the time-evolved reduced density matrix of the central subsystem and its stationary state, which is the thermal state at the bath temperature. Exploiting the free-fermionic structure of both models, the dynamics remains Gaussian and the Frobenius distance can be expressed exactly in terms of two-point correlation functions. Combining this representation with generalised hydrodynamics, we derive analytical predictions for the Frobenius distance in the hydrodynamic limit, providing a complete characterisation of the thermalisation process. Using these results, we investigate the possible occurrence of the Mpemba effect. We find that, despite the genuine non-equilibrium dynamics displayed by the system, no Mpemba effect arises in this setting. Our analysis identifies a broad class of boundary-driven thermalisation protocols in which relaxation is fully characterised analytically and exhibits no anomalous acceleration of equilibration.

Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2606.06362 [cond-mat.stat-mech]

(or arXiv:2606.06362v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2606.06362 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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