Spectral and Steady-State Properties of Random Liouvillians
arXiv:1905.02155 · doi:10.1088/1751-8121/ab9337
Abstract
We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We establish that the global spectral features, the spectral gap, and the steady-state properties follow three different regimes as a function of the dissipation strength, whose boundaries depend on the particular quantity. Within each regime, we determine the scaling exponents with the dissipation strength and system size. We find that, for two or more dissipation channels, the spectral gap increases with the system size. The spectral distribution of the steady state is Poissonian at low dissipation strength and conforms to that of a random matrix once the dissipation is sufficiently strong. Our results can help to understand the long-time dynamics and steady-state properties of generic dissipative systems.
arXiv comment21 pages, 11 figures. v2: minor corrections. v3: additional details, as published
References in corpus (34)
- Random-Matrix Theory of Quantum Transport
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Random Matrix Theories in Quantum Physics: Common Concepts
- Symmetry and Topology in Non-Hermitian Physics
- Matrix Product Density Operators: Simulation of finite-T and dissipative systems
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Induced measures in the space of mixed quantum states
- Solution of a minimal model for many-body quantum chaos
- Exact nonequilibrium steady state of a strongly driven open XXZ chain
- Markovian master equations for quantum thermal machines: local vs global approach
- Matrix product simulations of non-equilibrium steady states of quantum spin chains
- Non-Hermitean Random Matrix Theory: method of hermitization
- Tenfold Way for Quadratic Lindbladians
- Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
- Many-body quantum chaos: Analytic connection to random matrix theory
- Eigenvalue statistics of the real Ginibre ensemble
- Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
- Statistical properties of random density matrices
- Universal spectra of random Lindblad operators
- Exact Nonequilibrium Steady State of an Open Hubbard Chain
- Spectral gaps and mid-gap states in random quantum master equations
- Extreme Decoherence and Quantum Chaos
- Integrable quantum dynamics of open collective spin models
- Noisy Spins and the Richardson-Gaudin Model
- Non-Markovian effects in electronic and spin transport
- Universality of quantum Brownian motion
- Random transition-rate matrices for the master equation
- On random symmetric matrices with a constraint: the spectral density of random impedance networks
- Fate of in-medium heavy quarks via a Lindblad equation
- A random matrix theory of decoherence
- Improving coherence with nested environments
- Random density matrices versus random evolution of open systems
Cited by in corpus (46)
- Non-Hermitian Physics
- Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics
- Quantum Dynamics in Krylov Space: Methods and Applications
- Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
- Lindbladian dissipation of strongly-correlated quantum matter
- Lindbladian dynamics of the Sachdev-Ye-Kitaev model
- Field Theory of Many-Body Lindbladian Dynamics
- Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
- Spectral transitions and universal steady states in random Kraus maps and circuits
- Spectral Properties of Disordered Interacting Non-Hermitian Systems
- Many-body Hierarchy of Dissipative Timescales in a Quantum Computer
- Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
- Solving the Liouvillian Gap with Artificial Neural Networks
- Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
- Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
- From integrability to chaos in quantum Liouvillians
- Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
- Distinguishing between quantum and classical Markovian dephasing dissipation
- Robustness of quantum chaos and anomalous relaxation in open quantum circuits
- Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer
- Random matrix theory for quantum and classical metastability in local Liouvillians
- BROTOCs and Quantum Information Scrambling at Finite Temperature
- Spectral and steady-state properties of fermionic random quadratic Liouvillians
- Edge modes and symmetry-protected topological states in open quantum systems
- Quantum Chaos and Coherence: Random Parametric Quantum Channels
- Dissipative Quantum Chaos unveiled by Stochastic Quantum Trajectories
- Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
- Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
- Decoherence rate in random Lindblad dynamics
- Fuzzy measurements and coarse graining in quantum many-body systems
- Higher-order gap ratios of singular values in open quantum systems
- Non-equilibrium boundary driven quantum systems: models, methods and properties
- Localization of Lindbladian Fermions
- Random sparse generators of Markovian evolution and their spectral properties
- Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
- Transient and steady-state chaos in dissipative quantum systems
- Random Lindblad operators obeying detailed balance
- Integrability versus chaos in the steady state of many-body open quantum systems
- Dissipative chaos and steady state of open Tavis-Cummings dimer
- Correspondence principle, dissipation, and Ginibre ensemble
- Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
- Symmetry classification correspondence between quadratic Lindbladians and their steady states
- Open-system dynamics in local Lindbladians with chaotic spectra
- Measurement and feedforward induced entanglement negativity transition
- Quantum Lyapunov exponents and complex spacing ratios: two measures of Dissipative Quantum Chaos
- Variational Quantum Algorithm for Solving the Liouvillian Gap