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.
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.
The quantum Mpemba effect (QME) describes the counterintuitive phenomenon in which a system farther from equilibrium reaches steady state faster than one closer to equilibrium. However, ambiguity in defining a suitable distance measure between quantum states has led to varied interpretations across different contexts. Here we propose the intrinsic quantum Mpemba effect (IQME), defined using the trajectory length traced by the quantum state as a more appropriate measure of distance--distinct from previous trajectory-independent metrics. By treating quantum states as points in a Riemannian space defined by statistical distance, the trajectory length emerges as a more natural and accurate characterization of the counterintuitive dynamics, drawing an analogy to the classical Brachistochrone problem. We demonstrate the existence of IQME in Markovian systems and extend its definition to quantum circuits, thereby establishing a unified framework applicable to both open and closed systems. Notably, we observe an IQME in a U(1)-symmetric circuit, offering new insights into the rates of quantum thermalization for different initial states. This work deepens our understanding of quantum state evolution and lays the foundation for accurately capturing novel quantum dynamical behaviour.
Since its rediscovery in the twentieth century, the Mpemba effect, where a far-from-equilibrium state may relax faster than a state closer to equilibrium, has been extensively studied in classical systems and has recently received attention in quantum systems. Many theories explaining this counter-intuitive behavior in classical systems rely on memory effects. However, in quantum systems, the relation between the Mpemba effect and memory has remained unexplored. In this Letter, we consider general non-Markovian open quantum systems and reveal new classes of quantum Mpemba effects, with no analog in Markovian quantum dynamics. Generically, open quantum dynamics possess a finite memory time and a unique steady state. Because of non-Markovian dynamics, even if the system is initialized in the steady state it can take a long time to relax back. We find other initial states that reach the steady state much faster. Most notably, we demonstrate that there can be an initial state in which the system reaches the steady state within the finite memory time itself, giving the fastest possible relaxation to stationarity. We verify the effect for quantum dot systems coupled to electronic reservoirs in equilibrium and nonequilibrium setups at weak, intermediate and strong coupling. Our Letter provides new insights into the rich physics underlying accelerated relaxation in quantum systems.
Quantum Mpemba effect describes an anomalous phenomenon of accelerated relaxation which is of fundamental interest in the field of nonequilibrium thermodynamics. Conventional theories on this phenomenon strongly rely on the Born-Markovian approximation resulting in a Lindblad-type master equation whose evolution is governed by a Liouvillian superoperator. It has been demonstrated that exceptional points of the Liouvillian superoperator can induce the Mpemba effect in Markovian regimes. Moving beyond this Markovian limit, we here propose a mechanism for realizing the quantum Mpemba effect in a general non-Markovian relaxation process by means of non-Markovian exceptional points. We verify the feasibility of this mechanism within a dissipative quantum harmonic oscillator model, which is exactly solvable and experimentally practical. Providing new insight into the interesting non-equilibrium dynamics, our work paves a way to accelerate the transfer of energy and information in quantum 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.
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.
Abstract The quantum Mpemba effect (QMPE) is characterized by a state initially farther from equilibrium relaxing faster than one closer to it. In this work, we investigate the QMPE in an open central-spin model, and examine whether the QMPE emerges when the spins’ system is subjected to their independent noisy environment for different initial states. Simultaneously, we analyze the influence of the noisy environment on the dynamics and demonstrate that tuning local noise strengths can induce the QMPE. Furthermore, we systematically explore finite-size effects by varying the number of peripheral spins. In addition, we investigate the Pontus Mpemba effect within the same framework, demonstrating that an auxiliary decohering environment can accelerate the approach to stationarity. To observe the effect, we select the trace distance, energy, and l 1 -norm coherence as observables. By combining initial-state engineering (global rotation operations) with the modulation of the noisy environment, we clearly reveal the physical mechanisms for inducing and controlling the QMPE in this model. Our results show that both rotating the initial states and applying non-uniform local noises can alter the relaxation rate ordering among different states, leading to crossings in the evolution curves of various physical quantities, that is, the realization of the QMPE. This finding provides a new perspective for manipulating anomalous relaxation behavior in the quantum many-body system and open quantum system.