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 ‐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.
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 ‐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.
The quantum Mpemba effect (QME) describes the counterintuitive phenomenon where a system initially further from equilibrium relaxes faster than one closer to it. Specifically, the QME associated with symmetry restoration has been extensively investigated across integrable, ergodic, and disordered localized systems. However, its fate in disorder-free ergodicity-breaking settings, such as the Stark many-body localized (Stark-MBL) phase, remains an open question. Here, we explore the dynamics of local U(1) symmetry restoration in a Stark-MBL XXZ spin-12 chain, using the Rényi-2 entanglement asymmetry (EA) as a probe. Using an analytical operator-string expansion supported by numerical simulations, we demonstrate that the QME transitions from an initial-state-dependent anomaly in the ergodic phase to a universal feature in the Stark-MBL regime. Moreover, the Mpemba time scales exponentially with the subsystem size, even in the absence of global transport, and is governed by high-order off-resonant processes. We attribute this robust inversion to a Stark-induced hierarchy of relaxation channels that fundamentally constrains the effective Hilbert space dimension. The findings pave the way for utilizing tunable potentials to engineer and control anomalous relaxation timescales in quantum technologies without reliance on quenched disorder.
The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, non-Markovian memory, and initial system-reservoir entanglement. Here, we unveil a distinct mechanism rooted in the non-normal nature of the Liouvillian superoperator in Markovian dynamics. When the Liouvillian's eigenmodes are non-orthogonal, transient interference between decaying modes can induce anomalous early-time behavior-such as delayed thermalization or transient freezing-even though asymptotic decay rates remain unchanged. This differs fundamentally from strong Mpemba effects, which hinge on suppressed overlap with slow-decaying modes. We demonstrate this mechanism using a waveguide quantum electrodynamics model, where quantum emitters interact with the photonic modes of a one-dimensional waveguide. The directional and radiative nature of these couplings naturally introduces non-normality into the system's dynamics. As a result, certain initial states-despite being closer to equilibrium-can exhibit slower relaxation at short times. This work reveals a previously unexplored and universal source of Mpemba-like behavior in memoryless quantum systems, expanding the theoretical framework for anomalous relaxation and opening new avenues for control in engineered quantum platforms.
ABSTRACT The Mpemba effect is the counterintuitive phenomenon, where some states relax faster than others despite being initially farther from equilibrium. In quantum systems, realizing this effect typically requires fine‐tuned dissipation or carefully engineered initial states, making it fragile to disorder. Here, we uncover a robust statistical quantum Mpemba effect arising from Griffiths rare‐region physics in a one‐dimensional dissipative lattice. Sparse local losses fragment the system into random loss‐free regions that host long‐lived quasi‐bound modes with broadly distributed lifetimes. We show that simple extended Bloch states, although having identical density profiles, couple very differently to these modes: a uniform state predominantly excites slowly decaying modes, while a phase‐modulated state couples more strongly to rapidly decaying ones. This mismatch produces a disorder‐robust inversion of relaxation times, where the initially “farther” state relaxes faster. Our results identify Griffiths rare‐region physics as a robust mechanism for quantum Mpemba dynamics in disordered quadratic open quantum systems.
Relaxation towards equilibrium is often assumed to be slower when a system starts farther from equilibrium, but this intuition fails in the Mpemba effect. Recent advances in controllable quantum platforms have enabled the exploration of its quantum analogue, the quantum Mpemba effect (QME), yet its microscopic origin remains largely unclear. Here we provide a general framework for understanding the QME in closed quantum many-body chaotic systems by reformulating the equilibration process of local subsystems in terms of Ruelle-Pollicott (RP) resonances. We show that suppressing the initial-state overlap with the dominant RP resonant mode accelerates subsystem equilibration and thereby yields the QME. We further uncover that a novel type of strong QME can occur via complete translation-symmetry breaking of initial states. We substantiate our predictions using the prototypical kicked Ising chain and a quantum automaton circuit. These findings cast the QME in closed many-body systems into a unified framework with open-system analogues and provide experimentally accessible signatures on state-of-the-art quantum platforms.
The Mpemba effect, where a system initially farther from equilibrium relaxes faster than one closer to equilibrium, has been extensively studied in classical systems and recently explored in quantum settings. While previous studies of the quantum Mpemba effect (QME) have largely focused on isolated systems with global symmetries, we argue that the QME is ubiquitous in generic, nonintegrable many-body systems lacking such symmetries, including U(1) charge conservation, spatial symmetries, and even energy conservation. Using paradigmatic models such as the quantum Ising model with transverse and longitudinal fields, we show that the QME can be understood through the energy density of initial states and their inverse participation ratio in the energy eigenbasis. Our findings provide a unified framework for the QME, linking it with classical thermal relaxation.
We investigate the quantum Mpemba effect in the relaxation of open quantum systems whose effective dynamics is described by Davies maps. We introduce a class of unitary transformations constructed from permutation matrices that, when applied to an initial state, (i) suppress the slowest decaying modes of the nonunitary dynamics and (ii) maximize the state's distinguishability from the steady state. The first condition ensures exponentially faster convergence to equilibrium, while the second implies that a quantum system initially further from equilibrium can approach it more rapidly than one that starts closer. This protocol thus realizes a genuine Mpemba effect, and its simulation requires low computational effort. We prove that, for any initial state, there exists a permutation matrix that maximizes its distance from equilibrium with respect to a chosen information-theoretic distinguishability measure. We illustrate our findings for a two-level system, as well as for the nonunitary dynamics of the transverse-field Ising chain and the XXZ chain, each weakly coupled to a bosonic thermal bath. In these cases, the quantum Mpemba effect is demonstrated using the Hilbert-Schmidt distance, quantum relative entropy, and trace distance. Overall, our results provide a versatile framework for engineering a genuine quantum Mpemba effect in Markovian open quantum systems.