Skin Effect in Quadratic Lindbladian Systems: an Adjoint Fermion Approach

Abstract

The skin effect has been discovered in non-Hermitian Hamiltonian systems where all the eigenstates have their amplitudes concentrating to the open boundaries of the systems and decaying exponentially into the bulk. Later, certain open systems obeying the quadratic Lindblad equation has also been found to exhibit the skin effect, which is manifested in the ``chiral damping" phenomenon as the particle populations, decaying from their initial uniform unity values, show asymmetry with respect to the open boundaries. However, in those open systems, each cell couples to the environment in an identical way. It is natural to expect that the long time steady state of those open systems shall have spatially uniform particle populations. Furthermore, particle population variations due to the excitation of normal modes on top of the steady state shall also not show asymmetry with respect to the open boundaries. To reconcile the natural expectations with the skin effect, we employ an adjoint fermion formalism to study the quadratic Lindbladian systems. We work out the long time steady state and the normal modes on top of it, which exhibit no asymmetry as expected. We show that it is the interference between the normal modes that gives rise to the skin effect.

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• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Topological enhancement of non-normality in non-Hermitian skin effects
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Phase transitions in a non-Hermitian Su-Schrieffer-Heeger model via Krylov spread complexity
• Lindbladian versus Postselected Non-Hermitian Topology
• Majorana zero-modes in a dissipative Rashba nanowire
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures