Closed chaotic quantum systems relax after a quench into a Gibbs ensemble. At late times, the relaxation speed is determined by their conservation laws and hydrodynamics. As a result, there exist pairs of initial states which thermalize to the same ensemble, yet exhibit drastically different hydrodynamic relaxation. We show in two chaotic spin chains how this enables a simple and robust realization of the quantum Mpemba effect: a system initially closer to equilibrium relaxes slower than one that starts farther away, despite both approaching the same final state.
Closed chaotic quantum systems relax after a quench into a Gibbs ensemble. At late times, the relaxation speed is determined by their conservation laws and hydrodynamics. As a result, there exist pairs of initial states which thermalize to the same ensemble, yet exhibit drastically different hydrodynamic relaxation. We show in two chaotic spin chains how this enables a simple and robust realization of the quantum Mpemba effect: a system initially closer to equilibrium relaxes slower than one that starts farther away, despite both approaching the same final state.
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.
Observation of the quantum Mpemba effect has spurred much interest in its enabling conditions and its relation to the classical counterpart. Here, we consider weakly open many-body quantum systems initialized in different thermal states and examine when the initially farther state relaxes to the (non-equilibrium) steady state faster. We claim that the number of conserved quantities in the unitary part plays a crucial role: the Mpemba effect is possible only when the Hamiltonian commutes with other extensive operators or is integrable. The reason lies in the dynamical evolution happening in spaces of different dimensions. When energy is the only approximately conserved quantity, dissipation pushes the dynamics within a single-parameter manifold of different thermal states. In contrast, for Hamiltonians with several conserved quantities, the dynamics drift in the multi-dimensional space of generalized Gibbs ensembles, whose distance to the steady state is less trivial. We provide numerical results for large system sizes using tensor networks and free-fermion techniques, thereby supporting our claim.
The Mpemba effect, where a state farther from equilibrium relaxes faster than one closer to it, is a striking phenomenon in both classical and quantum systems. In open quantum systems, however, the quantum Mpemba effect (QME) typically occurs only for specifically chosen initial states, which limits its universality. Here we present a general and experimentally feasible strategy to realize both QME and anti-QME. By applying a temporary bond-dissipation quench, we selectively suppresses or enhances slow relaxation modes, thereby reshaping relaxation pathways independently of both the system and the initial state. We demonstrate this mechanism in systems with dephasing and boundary dissipation, and outline feasible cold-atom implementations. Our results establish controllable dissipation as a versatile tool for quantum control, accelerated relaxation, and efficient nonequilibrium protocols.
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.
The Mpemba effect, where a state prepared farther from equilibrium relaxes faster to equilibrium than one prepared closer, has a quantum counterpart where relaxation is resolved by conserved charge. However, the fate of the quantum Mpemba effect in systems with long-range interactions remains an open question. Here, we study the quantum Mpemba effect in long-ranged, U(1)-symmetric random unitary circuits. Using annealed Rényi-2 entanglement asymmetry computed via replica tensor networks and exact diagonalization, we track the symmetry restoration from three types of tilted product states: ferromagnetic, antiferromagnetic, and ferromagnetic with a central domain wall. The quantum Mpemba effect is present for tilted ferromagnetic states at all interaction ranges, but absent for tilted antiferromagnetic states, and occurs for the domain-wall state only in effectively short-ranged circuits, where the Mpemba time tM is found to scale with the subsystem size NA as tM∼NAz, with the dynamical exponent z=min(α−1,2). These results reveal how the quantum Mpemba effect is governed by the interplay between interaction range and initial-state charge bias in long-ranged chaotic systems.
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.