Quantum Pontus--Mpemba Effect in Dissipative Quasiperiodic Chains

Abstract

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.

Figures (6)

• Figure 1: (a) Fractal dimension $D_q$ as a function of eigenenergy $E$ and quasidisorder strength $V$. Black dashed lines indicate the analytical mobility edges, and the red dashed line marks the critical point $V=1$. (b) Time evolution of the trace distance $D_{\mathrm{tr}}$ under pure dephasing for a localized eigenstate ($E=-2.03$, orange) and an extended eigenstate ($E=0.35$, blue). Inset: overlap of each eigenstate with the slowest Liouvillian decay mode. (c),(d) Spatial density distributions corresponding to the localized and extended eigenstates in (b). Parameters: $\beta=(\sqrt{5}-1)/2$, $t=1$, $V=1$, $\Gamma_1=0.1$. System size: $L=610$ in (a) and $L=40$ in (b)–(d).
• Figure 2: PME in the localized regime. (a), (b) Time evolution of the trace distance $D_{\mathrm{tr}}$ for the two-step protocol (orange: weak coupling to a finite-temperature Ohmic bath) and the direct one-step protocol (blue: pure dephasing). The prethermalization duration is chosen as one-fifth of the total evolution time, with a weak auxiliary coupling $\Gamma_2=\Gamma_1/100$ and bath temperature $T=1$. Panel (a): $7\mathrm{th}$ eigenstate ($E=-1.98$, $T_{\mathrm{eff}}=1.10$); panel (b): $12\mathrm{th}$ eigenstate ($E=-1.18$, $T_{\mathrm{eff}}=2.35$). Insets show the overlaps of the initial and intermediate states with the slowest Liouvillian decay mode. (c), (d) Corresponding control results with the quasiperiodic potential removed ($V=0$). Other parameters are identical to Fig. \ref{['fig1']}.
• Figure 3: PME in the extended regime. (a) Dynamics of the 17th eigenstate ($E=-0.33$, $T_{\mathrm{eff}}=10.43$) prethermalized by a bath at $T=2$. (b) Dynamics of the 20th eigenstate ($E=-0.08$, $T_{\mathrm{eff}}=135.74$) prethermalized at $T=7$. In both cases the prethermalization duration is chosen as one-tenth of the total evolution time, with a weak auxiliary coupling $\Gamma_2=\Gamma_1/250$ and bath temperature $T=1$. (c),(d) Corresponding results in the clean limit ($V=0$). Orange (blue) curves denote the two-step (one-step) scheme.
• Figure 4: Spectral mechanism underlying the acceleration. (a),(b) Absolute overlaps between Liouvillian decay modes and two states: the initial eigenstate (blue) and the intermediate thermal state (orange). Panel (a) corresponds to the 12th eigenstate and a thermal state at $T=1$; panel (b) to the 17th eigenstate and a thermal state at $T=2$. (c) Overlap between thermal states at different temperatures and the slowest decay mode. Inset: $1\le T\le10$.
• Figure 5: Relaxation dynamics in the generalized Aubry--André model with power-law hopping. (a) Phase diagram in the $(V,a)$ plane for $L=987$ and $t=1$. The dashed line denotes the conventional AA boundary $V=2t$, while the solid horizontal line marks $a=1$. The red star indicates the parameter set used in panels (b)--(d). (b) Time evolution of the trace distance $D_{\mathrm{tr}}$ under pure dephasing with rate $\Gamma_1=0.1$, starting from a localized eigenstate (22nd, orange) and an extended eigenstate (57nd, blue) at $L=90$, $t=1$, and $V=1.1$. A crossover in the relaxation curves is observed, signaling Mpemba-like behavior. The inset shows the projection of each initial state onto the slowest Liouvillian decay mode. (c),(d) Spatial particle-density profiles of the localized and extended eigenstates in (b), respectively. Here $\beta=(\sqrt{5}-1)/2$ and periodic boundary conditions are used.