Erratic Liouvillian Skin Localization and Subdiffusive Transport

TL;DR

This paper explores how globally reciprocal Liouvillian dynamics lead to erratic localization and ultra-slow subdiffusive transport, revealing fundamental differences from non-Hermitian Hamiltonian systems.

Contribution

It demonstrates that in Liouvillian systems, erratic localization coexists with subdiffusive transport, a behavior not observed in Hamiltonian models.

Findings

Steady state shows disorder-dependent, erratic localization without boundary accumulation.

Excitations spread via Sinai-type subdiffusion, much slower than normal diffusion.

Liouvillian systems uniquely exhibit coexistence of erratic localization and ultra-slow transport.

Abstract

Non-Hermitian systems with globally reciprocal couplings -- such as the Hatano-Nelson model with stochastic imaginary gauge fields -- avoid the conventional non-Hermitian skin effect, displaying erratic bulk localization while retaining ballistic transport. An open question is whether similar behavior arises when non-reciprocity originates at the Liouvillian level rather than from an effective non-Hermitian Hamiltonian obtained via post-selection. Here, a lattice model with globally reciprocal Liouvillian dynamics and locally asymmetric incoherent hopping is investigated, a disordered setting in which Liouvillian-specific effects have remained largely unexplored. While the steady state again shows disorder-dependent, erratic localization without boundary accumulation, {\color{black}excitations in the incoherent-hopping regime spread via {\em Sinai-type subdiffusion}, dramatically slower than ordinary diffusion in symmetric stochastic lattices.} {\color{black}This highlights that the genuinely distinct Liouvillian signature is the coexistence of global reciprocity with ultra-slow, disorder-induced subdiffusive transport, rather than the erratic localization itself.} {\color{black}These results reveal a fundamental distinction between globally reciprocal Hamiltonian and Liouvillian systems: in both cases the skin effect is suppressed, but only in Liouvillian dynamics erratic skin localization can coexist with subdiffusive transport