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.

References in corpus (7)

• Topological Origin of Non-Hermitian Skin Effects
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Non-equilibrium phase transition in a periodically driven XY spin chain
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics

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• 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