Unraveling the Non-Hermitian Skin Effect in Dissipative Systems

• URL: http://arxiv.org/abs/2010.12431v1
• Date: Fri, 23 Oct 2020 14:23:16 GMT
• Title: Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Authors: Stefano Longhi
• Abstract summary: The non-Hermitian skin effect is an exotic manifestation of non-Hermitian systems. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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