Erratic Liouvillian Skin Localization and Subdiffusive 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 we investigate this scenario in a lattice model with globally reciprocal Liouvillian dynamics and locally asymmetric incoherent hopping, 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, we find that global reciprocity in the Liouvillian does not protect transport. Instead, in the regime dominated by incoherent hopping, excitations spread via Sinai-type subdiffusion, dramatically slower than the ordinary diffusion found in symmetric stochastic lattices. Our results reveal a fundamental distinction between globally reciprocal Hamiltonian and Liouvillian dynamics: global reciprocity suppresses the skin effect in both cases, but only in Liouvillian dynamics can it coexist with ultra-slow, disorder-induced subdiffusive transport.