Unraveling the Non-Hermitian Skin Effect in Dissipative Systems

TL;DR

This paper investigates the non-Hermitian skin effect in dissipative systems, revealing that while the effect is washed out in a full quantum description, it leaves a hidden signature in the relaxation dynamics toward a maximally mixed state.

Contribution

It demonstrates that the non-Hermitian skin effect is suppressed in a self-consistent quantum dissipative framework but can be inferred from relaxation dynamics, bridging semiclassical and quantum descriptions.

Findings

Skin effect is washed out in quantum dissipative models.

Relaxation dynamics reveal hidden signatures of the skin effect.

Maximally mixed state relaxation relates to the semiclassical skin effect.

Abstract

The non-Hermitian skin effect, i.e. eigenstate condensation at the edges in lattices with open boundaries, is an exotic manifestation of non-Hermitian systems. In Bloch theory, an effective non-Hermitian Hamiltonian is generally used to describe dissipation, which however is not norm-preserving and neglects quantum jumps. Here it is shown that in a self-consistent description of the dissipative dynamics in a one-band lattice, based on the stochastic Schr\"odinger equation or Lindblad master equation with a collective jump operator, the skin effect and its dynamical features are washed out. Nevertheless, both short- and long-time relaxation dynamics provide a hidden signature of the skin effect found in the semiclassical limit. In particular, relaxation toward a maximally mixed state with the largest von Neumann entropy in a lattice with open boundaries is a manifestation of the semiclassical skin effect.