We investigate how quasiperiodic spatial structure enables protocol-induced acceleration in open quantum systems by analyzing the Pontus-Mpemba effect in one-dimensional chains subject to Markovian dephasing. The dynamics are governed by a Lindblad superoperator that drives all initial states toward a maximally mixed infinite-temperature steady state, isolating dynamical mechanisms from static equilibrium properties. Considering two representative quasiperiodic models, namely a tight-binding chain with a mosaic potential and its extension with power-law long-range hopping, we show that a properly engineered two-step protocol, in which the system is first steered to a finite temperature intermediate state, yields a strictly shorter overall relaxation time than direct evolution from the same initial configuration. This protocol-induced acceleration persists for both initially localized and extended eigenstates and remains robust in the presence of long-range hopping. A Liouvillian spectral analysis reveals that the mechanism originates from a redistribution of spectral weight that suppresses overlap with the slowest decay modes, rather than from any modification of the decay spectrum itself. Our results establish quasiperiodic chains as a controlled setting for engineering relaxation pathways through Liouvillian spectral structure.
We investigate how quasiperiodic spatial structure enables protocol-induced acceleration in open quantum systems by analyzing the Pontus-Mpemba effect in one-dimensional chains subject to Markovian dephasing. The dynamics are governed by a Lindblad superoperator that drives all initial states toward a maximally mixed infinite-temperature steady state, isolating dynamical mechanisms from static equilibrium properties. Considering two representative quasiperiodic models, namely a tight-binding chain with a mosaic potential and its extension with power-law long-range hopping, we show that a properly engineered two-step protocol, in which the system is first steered to a finite temperature intermediate state, yields a strictly shorter overall relaxation time than direct evolution from the same initial configuration. This protocol-induced acceleration persists for both initially localized and extended eigenstates and remains robust in the presence of long-range hopping. A Liouvillian spectral analysis reveals that the mechanism originates from a redistribution of spectral weight that suppresses overlap with the slowest decay modes, rather than from any modification of the decay spectrum itself. Our results establish quasiperiodic chains as a controlled setting for engineering relaxation pathways through Liouvillian spectral structure.
We unveil a quantum Pontus-Mpemba effect enabled by the Liouvillian skin effect in a dissipative tight-binding chain with asymmetric incoherent hopping and coherent boundary coupling. The skin effect, induced by non-reciprocal dissipation, localizes relaxation modes near the system boundaries and gives rise to non-orthogonal spectral geometry. While such non-normality is often linked to slow relaxation, we show that it can instead accelerate relaxation through a two-step protocol - realizing a quantum Pontus-Mpemba effect. Specifically, we consider a one-dimensional open chain with coherent hopping J, asymmetric incoherent hoppings JR=JL, and a controllable end-to-end coupling ε. For ε=0, the system exhibits the Liouvillian skin effect, with left and right eigenmodes localized at opposite edges. We compare two relaxation protocols toward the same stationary state: (i) a direct relaxation with ε=0, and (ii) a two-step (Pontus) protocol where a brief coherent evolution transfers the excitation across the lattice before relaxation. Although both share the same asymptotic decay rate, the two-step protocol relaxes significantly faster due to its reduced overlap with the slow boundary-localized Liouvillian mode. The effect disappears when JR=JL, i.e., when the skin effect vanishes. Our results reveal a clear connection between boundary-induced non-normality and protocol-dependent relaxation acceleration, suggesting new routes for controlling dissipation and transient dynamics in open quantum systems.
The slowest Liouvillian mode often bottlenecks the relaxation of an open quantum system to its steady state. Standard strategies circumvent this bottleneck by selecting special initial states or engineering the dissipator. Here we show that neither is necessary. We introduce a pre-dissipative geometric steering protocol that reshapes any given pure or mixed state before relaxation begins -- coherent rotations interleaved with nonselective projective measurements -- at fixed Lindblad generator. By steering the state's Bloch direction along geodesic paths, the protocol suppresses its overlap with the slowest Liouvillian modes. The prepared state then starts farther from equilibrium yet relaxes faster, realizing the quantum Mpemba effect, whenever two computable conditions hold: reduced slow-mode overlap and a larger initial distance to stationarity. Our framework treats real and complex spectral gaps uniformly, and we demonstrate robust Mpemba acceleration in driven qubit and multiqubit systems using operations available in trapped-ion and superconducting platforms.
The classical Mpemba effect is the counterintuitive phenomenon where hotter water freezes faster than colder water due to the breakdown of Newton's law of cooling after a sudden temperature quench. The genuine nonequilibrium post-quench dynamics allows the system to evolve along effective shortcuts absent in the quasi-static regime. When the time needed for preparing the (classical or quantum) system in the hotter initial state is included, we encounter so-called Pontus-Mpemba effects. We here investigate multi-step Pontus-Mpemba protocols for open quantum systems whose dynamics is governed by non-autonomous (aka time-inhomogeneous) Lindblad master equations. In the limit of infinitely many steps, one arrives at continuous Pontus-Mpemba protocols. We study the crossover between the quasi-static and the sudden-quench regime, showing the presence of dynamically generated shortcuts achieved for time-dependent dissipation rates. Considering a two-parameter family of time-dependent rates, the parameters allowing for optimal speed-up conditions are determined. Time-dependent rates can also cause non-Markovian behavior, highlighting the existence of rich dynamical regimes accessible beyond the Markovian framework.
We study a one-dimensional quasiperiodic tight-binding model with simultaneous off-diagonal (hopping) and diagonal (onsite) modulations. Using the inverse participation ratio and the wave-packet centroid, we construct localization-delocalization phase diagrams for both equilibrium and nonequilibrium steady states. We analyze the robustness of initial-state properties under dissipation and characterize dissipation-induced localization-delocalization transitions (and their reversals) in detail. Trace-distance dynamics provide evidence for a quantum Mpemba effect: states prepared farther from the steady state can relax faster than states initialized closer to it. We propose a starting-line hypothesis that explains the presence or absence of this effect across parameter regimes. These results advance the understanding of steady-state phase transitions and relaxation dynamics in dissipatively driven quasiperiodic systems.
CStrong quantum Mpemba acceleration requires suppressing the slowest visible Liouvillian relaxation channel, but a robust many-body mechanism for enforcing such suppression remains challenging. We identify such a mechanism in locally dephased constrained Rydberg chains through exact slow-mode selection. For constrained single-spin-flip Hamiltonians, local dephasing turns the Hamiltonian itself into an exact left Liouvillian eigenmode, L†(H)=−γH. A finite-temperature reference state generically overlaps with this H-like slow mode, whereas translationally invariant states with Tr(Hρ0)=0 remove it and are confined to the Q=0 operator sector. When the next visible Q=0 mode decays faster, these selected states exhibit a strong quantum Mpemba effect. We demonstrate this mechanism in the PXP chain for a zero-energy scar eigenstate, the all-zero product state, and a translation-invariant Z2 cat state, and show that it persists in the (2,3) model and the longer-range blockade family. Our results identify Liouvillian mode visibility, rather than special scar wave functions, as the organizing principle for anomalously fast relaxation in constrained open quantum systems.
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.