Full spectrum of the Liouvillian of open dissipative quantum systems in the Zeno limit

Abstract

We consider an open quantum system with dissipation, described by a Lindblad Master equation (LME). For dissipation locally acting and sufficiently strong, a separation of the relaxation time scales occurs, which, in terms of the eigenvalues of the Liouvillian, implies a grouping of the latter in distinct vertical stripes in the complex plane at positions determined by the eigenvalues of the dissipator. We derive effective LME equations describing the modes within each stripe separately, and solve them perturbatively, obtaining for the full set of eigenvalues and eigenstates of the Liouvillian explicit expressions correct at order $1/\Gamma$ included, where $\Gamma$ is the strength of the dissipation. As a example, we apply our general results to quantum $XYZ$ spin chains coupled, at one boundary, to a dissipative bath of polarization.

arXiv commentLetter + Supplemental Material

References in corpus (22)

• Exceptional Topology of Non-Hermitian Systems
• The physics of exceptional points
• Finite-temperature transport in one-dimensional quantum lattice models
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• Turbo charging time-dependent density-functional theory with Lanczos chains
• Quantum Zeno effect by general measurements
• Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
• Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model
• Geometry and response of Lindbladians
• Measurement quantum mechanics and experiments on quantum Zeno effect
• Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
• Hierarchy of relaxation timescales in local random Liouvillians
• Spectral gaps and mid-gap states in random quantum master equations
• Exceptional points of the Lindblad operator of a two-level system
• Exact nonequilibrium steady state of open XXZ/XYZ spin-1/2 chain with Dirichlet boundary conditions
• Quantum Zeno Dynamics from General Quantum Operations
• Effective dynamics of strongly dissipative Rydberg gases
• Effective quantum Zeno dynamics in dissipative quantum systems
• Optomechanical damping basis
• Dissipative generation of pure steady states and a gambler's ruin problem
• Lie-algebraic approach to one-dimensional translationally invariant free-fermionic dissipative systems
• Diffusion and entanglement in open quantum systems

Cited by in corpus (16)

• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• Topological Quantum Batteries
• Hyper-acceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment
• Measurement Induced Continuous Time Crystals
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Hydrodynamics of quantum entropies in Ising chains with linear dissipation
• Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Quasiparticles of Decoherence Processes in Open Quantum Many-Body Systems: Incoherentons
• Exact solution of the boundary-dissipated transverse field Ising model: Structure of Liouvillian spectrum and dynamical duality
• Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
• Quantum control for the Zeno effect with noise
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Discovery of energy landscapes towards optimized quantum transport: Environmental effects and long-range tunneling
• Closed dynamical recursion equations for correlation functions and the application on the construction of Liouvillian spectrum in Lindbladian systems
• Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study