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Erratic Liouvillian skin localization and subdiffusive transport
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DOI：10.1088/2058-9565/ae5fcb.png)
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Abstract
En 中文
Non-Hermitian (NH) systems with globally reciprocal couplings—such as the Hatano–Nelson model with stochastic imaginary gauge fields—avoid the conventional NH 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 NH 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, excitations in the incoherent-hopping regime spread via Sinai-type subdiffusion, dramatically slower than ordinary diffusion in symmetric stochastic lattices. 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. 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.
Keywords:
Liouvillian dynamics
non-Hermitian systems
skin effect
subdiffusion
disorder localization
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