Quantum Pontus–Mpemba effect enabled by the Liouvillian skin effect

We unveil a quantum Pontus–Mpemba effect (PME) enabled by the Liouvillian skin effect (LSE) 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 PME. 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 LSE, 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.