Boundary sensitive Lindbladians and relaxation dynamics

Abstract

It is well known that non-Hermitian systems can be extremely sensitive to boundary conditions owing to non-Hermitian skin effect (NHSE). Analogously, we investigate two boundary-sensitive $U(1)$ symmetric Lindbladians: one carries current in the steady state, and the other does not. The numerical results indicate significant change of the Liouvillian spectrum, eigenmodes and relaxation time for both Lindbladians when the boundary conditions are altered. This phenomenon is found to be triggered by the Liouvillian skin effect (LSE), specifically the localization of eigenmodes, which stems from the NHSE of the non-Hermitian effective Hamiltonian. In addition, these two Lindbladians manifest different LSE, ultimately resulting in distinct relaxation behaviors.

19pages, 27 figures

References in corpus (23)

• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Topological Origin of Non-Hermitian Skin Effects
• An Open-System Quantum Simulator with Trapped Ions
• Quantum trajectories and open many-body quantum systems
• Non-Hermitian topological phenomena: A review
• Topological Non-Hermitian skin effect
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
• Liouvillian Skin Effect in an Exactly Solvable Model
• Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities
• Unusual Dynamical Properties of Disordered Polaritons in Micocavities
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Controlling entanglement at absorbing state phase transitions in random circuits
• Entanglement Steering in Adaptive Circuits with Feedback
• Symmetrized Liouvillian Gap in Markovian Open Quantum Systems
• Universal KPZ scaling in noisy hybrid quantum circuits
• Many-body non-Hermitian skin effect under dynamic gauge coupling
• Dynamic skin effects in non-Hermitian systems
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Absence of logarithmic and algebraic scaling entanglement phases due to skin effect
• Accelerating Relaxation Dynamics in Open Quantum System with Liouvillian Skin Effect
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Exceptional points and exponential sensitivity for periodically driven Lindblad equations

Cited by in corpus (9)

• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Lindbladian versus Postselected Non-Hermitian Topology
• Delocalization of skin steady states
• Optical pumping through the Liouvillian skin effect
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Closed dynamical recursion equations for correlation functions and the application on the construction of Liouvillian spectrum in Lindbladian systems
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures