Quantum Mpemba Effect in a Four-Site Bose-Hubbard Model

Abstract

We investigate relaxation-order inversion, known as the quantum Mpemba effect (QME), in a minimal open many-body system called a one-dimensional four-site Bose--Hubbard chain governed by Lindblad dynamics with local number dephasing. Families of thermal initial states are prepared at a fixed temperature and evolved under a common reference Liouvillian toward the same stationary state. Relaxation is characterized using four complementary diagnostics: trace distance, quantum relative entropy, symmetry-projected entropy imbalance (entanglement asymmetry), and the ${\ell }_1$-norm of coherence in the Fock basis. We find that QME emerges robustly in -the clean interacting regime, where on-site interactions redistribute the overlaps of initial states with slow Liouvillian decay modes, enabling states initially farther from equilibrium to converge faster at late times. In contrast, the noninteracting limit exhibits a monotonic relaxation hierarchy across all metrics. Introducing a linear Stark potential or random on-site disorder suppresses relaxation and eliminates QME signatures by inhibiting transport-assisted mixing and enhancing the dominance of slow modes. Within the explored parameter regime, the Stark field induces significantly stronger retardation than disorder. We further show that symmetry-projected entropy imbalance is particularly sensitive to charge-sector decoherence in reduced subsystems and provides a stringent probe of QME in bosonic platforms. Our results elucidate the essential role of interactions in enabling anomalous relaxation in open lattice systems and connect the suppression of QME under spatial inhomogeneity to localization phenomena in tilted and disordered Bose--Hubbard chains.

12 pages, 4 figures

References in corpus (32)

• Many-Body Physics with Ultracold Gases
• Cold bosonic atoms in optical lattices
• Quantifying Coherence
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Probing entanglement entropy via randomized measurements
• Controlling the dynamics of an open many-body quantum system with localized dissipation
• Stark many-body localization
• Anomalous cooling and heating - the Mpemba effect and its inverse
• Towards a theory of metastability in open quantum dynamics
• When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids
• Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect
• The Mpemba index and anomalous relaxation
• Microscopic origin of the quantum Mpemba effect in integrable systems
• Atom-light crystallization of BECs in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration
• QuTiP 5: The Quantum Toolbox in Python
• Symmetry restoration and quantum Mpemba effect in symmetric random circuits
• Observation of quantum strong Mpemba effect
• Thermodynamics of the quantum Mpemba effect
• The quantum Mpemba effects
• Quenches across the self-organization transition in multimode cavities
• Many-body interband tunneling as a witness for complex dynamics in the Bose-Hubbard model
• The quantum Mpemba effect in free-fermionic mixed states
• Thermomajorization Mpemba Effect
• Damped Bloch oscillations of cold atoms in optical lattices
• Mpemba effect and super-accelerated thermalization in the damped quantum harmonic oscillator
• Tuning the Quantum Mpemba Effect in Isolated System by Initial State Engineering
• Spectral analysis of two-dimensional Bose-Hubbard models
• Engineering many-body quantum dynamics by disorder
• Unravelling Metastable Markovian Open Quantum Systems
• Coherence, Transport, and Chaos in 1D Bose-Hubbard Model: Disorder vs. Stark Potential