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.
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.
In recent years, the quantum Mpemba effect (QME) which occurs when an out-of-equilibrium system reaches equilibrium faster than another that is closer to equilibrium has attracted significant attention from the scientific community as an intriguing and counterintuitive phenomenon. It generalizes its classical counterpart, extending the concept beyond thermal equilibration. This paper approaches the QME for Markovian open quantum systems from different perspectives. Firstly, we propose a physical mechanism based on decoherence-free subspaces. Secondly, we show that a macroscopic enhancement of the decay rate that scales linearly with system size can be obtained, leading to an extreme version of the phenomenon on Markovian open quantum systems. Thirdly, we study the Mpemba effect through the unravelings of Davies maps, revealing subtleties in the figures of merit which are chosen for obtaining the QME. Lastly, we propose a microscopic model for a better understanding of thermal bath dynamics in this context.
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 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.
Quantum Mpemba effect occurs when a quantum system, residing far away from the steady state, relaxes faster than a relatively nearer state. We look for the presence of this highly counterintuitive effect in the relaxation dynamics of the operators within the open quantum system setting. Since the operators evolve under a non-trace preserving map, the trace distance of an operator is not a monotonically decaying function of time, unlike its quantum state counterpart. Consequently, the trace distance can not serve as a reliable measure for detecting the Mpemba effect in operator dynamics. We circumvent this problem by defining a \textit{dressed} distance between operators that decays monotonically with time, enabling a generalized framework to explore the Mpemba-like effect for operators. Applying the formalism to various open quantum system settings, we find that, interestingly, in the single qubit case, only accelerated relaxation of operators is possible, while genuine Mpemba-like effects emerge in higher-dimensional systems such as qutrits and beyond. Furthermore, we demonstrate the existence of Mpemba-like effects in nonlocal, non-equilibrium operators, such as current, in a double-quantum-dot setup. Our results, besides offering fundamental insight about the occurrence of the Mpemba-like effect under non-trace preserving dynamics, open avenues for new experimental studies where quicker relaxation of observables could be of significant interest.
The Mpemba effect, in which a system farther from equilibrium relaxes faster than one closer to it, defies the intuition of nonequilibrium statistical mechanics. Here, we introduce a general framework to unambiguously witness this phenomenon based on a single observable defined for Markovian open quantum systems. The Mpemba observable bypasses full state tomography, offering utility for state preparation and thermal task optimization. We illustrate our method using local magnetization as a Mpemba signature, applying it to a qubit under generalized amplitude damping.
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.