Erratic Liouvillian Skin Localization and Subdiffusive Transport

• URL: http://arxiv.org/abs/2602.14698v1
• Date: Mon, 16 Feb 2026 12:38:31 GMT
• Title: Erratic Liouvillian Skin Localization and Subdiffusive Transport
• Abstract summary: We study non-reciprocity in a lattice model with globally reciprocal Liouvillian dynamics and locally asymmetric incoherent hopping.<n>We find that global reciprocity in the Liouvillian does not protect transport.<n>Our results reveal a fundamental distinction between globally reciprocal Hamiltonian and Liouvillian dynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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