Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect

TL;DR

This paper demonstrates a quantum effect where non-normality caused by the Liouvillian skin effect can accelerate relaxation in an open quantum chain through a two-step protocol, contrasting typical slow relaxation scenarios.

Contribution

It introduces the quantum Pontus-Mpemba effect enabled by the Liouvillian skin effect, showing how protocol design can leverage non-normality to speed up relaxation in dissipative quantum systems.

Findings

Two-step protocol significantly speeds up relaxation compared to direct relaxation.

The quantum Pontus-Mpemba effect occurs only with the Liouvillian skin effect present.

Relaxation acceleration is linked to boundary-induced non-normality.

Abstract

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 $J_{\rm R} \neq J_{\rm L}$, and a controllable end-to-end coupling $\epsilon$. For $\epsilon=0$, 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 $\epsilon=0$, 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 $J_{\rm R}=J_{\rm L}$, 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.