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arXiv · 2010.12431

Unraveling the Non-Hermitian Skin Effect in Dissipative Systems

Stefano Longhi
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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 Schrödinger 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.

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Stefano Longhi. 2020-10-23. Unraveling the Non-Hermitian Skin Effect in Dissipative Systems. https://doi.org/10.1103/physrevb.102.201103

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