Random Lindblad Dynamics
arXiv:1902.01442 · doi:10.1088/1751-8121/ab4d26
Abstract
We study the mixing behavior of random Lindblad generators with no symmetries, using the dynamical map or propagator of the dissipative evolution. In particular, we determine the long-time behavior of a dissipative form factor, which is the trace of the propagator, and use this as a diagnostic for the existence or absence of a spectral gap in the distribution of eigenvalues of the Lindblad generator. We find that simple generators with a single jump operator are slowly mixing, and relax algebraically in time, due to the closing of the spectral gap in the thermodynamic limit. Introducing additional jump operators or a Hamiltonian opens up a spectral gap which remains finite in the thermodynamic limit, leading to exponential relaxation and thus rapid mixing. We use the method of moments and introduce a novel diagrammatic expansion to determine exactly the form factor to leading order in Hilbert space dimension . We also present numerical support for our main results.
arXiv commentv2: 38 pages, 17 figures, with a few more substantial appendices elaborating upon the main results
References in corpus (64)
- Thermalization and its mechanism for generic isolated quantum systems
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Decoherence Free Subspaces for Quantum Computation
- The approach to thermal equilibrium in quantized chaotic systems
- Quantum speed limits in open system dynamics
- Decoherence, Chaos, and the Second Law
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Symmetries and conserved quantities in Lindblad master equations
- Spectral theory of Liouvillians for dissipative phase transitions
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Dissipative Phase Transition in Central Spin Systems
- Solution of a minimal model for many-body quantum chaos
- Algebraic versus exponential decoherence in dissipative many-particle systems
- Towards a theory of metastability in open quantum dynamics
- Relaxation times of dissipative many-body quantum systems
- Non-Hermitean Random Matrix Theory: method of hermitization
- Quantum phase transition in a far from equilibrium steady state of XY spin chain
- Loschmidt Echo
- Truncations of random unitary matrices
- Robustness of Decoherence-Free Subspaces for Quantum Computation
- Thouless and relaxation time scales in many-body quantum systems
- Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
- Kinetic constraints, hierarchical relaxation and onset of glassiness in strongly interacting and dissipative Rydberg gases
- Quantum logarithmic Sobolev inequalities and rapid mixing
- Universal spectra of random Lindblad operators
- Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
- Random matrix techniques in quantum information theory
- Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption
- On the time scales in the approach to equilibrium of macroscopic quantum systems
- Random Quantum Operations
- Random Unitaries Give Quantum Expanders
- Classical wave experiments on chaotic scattering
- A random matrix formulation of fidelity decay
- Resonance widths in open microwave cavities studied by harmonic inversion
- Nonhermitean Random Matrix Models : a Free Random Variable Approach
- Extreme Decoherence and Quantum Chaos
- Dissipative chaotic scattering
- Stability of local quantum dissipative systems
- Rapid mixing implies exponential decay of correlations
- Orthogonality catastrophe in dissipative quantum many body systems
- Spectral problems in open quantum chaos
- Experimental Observation of the Spectral Gap in Microwave n-Disk Systems
- Relaxation process in a regime of quantum chaos
- Effective quantum Zeno dynamics in dissipative quantum systems
- Random transition-rate matrices for the master equation
- Fingerprints of Classical Instability in Open Quantum Dynamics
- Eigenvalues of non-hermitian random matrices and Brown measure of non-normal operators: hermitian reduction and linearization method
- Spectral properties of noisy classical and quantum propagators
- Power-law approach to steady state in open lattices of non-interacting electrons
- Spectrum of Markov generators on sparse random graphs
- Non-Hermitean Random Matrix Theory: Summation of Planar Diagrams, the "Single-Ring" Theorem and the Disk-Annulus Phase Transition
- Lower bounds to the spectral gap of Davies generators
- Semiclassical Mechanism for the Quantum Decay in Open Chaotic Systems
- The Spectral Autocorrelation Function in Weakly Open Chaotic Systems: Indirect Photodissociation of Molecules
- Spectral properties and classical decays in quantum open systems
- Universality of spectra for interacting quantum chaotic systems
- A Matrix Model of Relaxation
- Rapid mixing and stability of quantum dissipative systems
- Spectral properties of Dissipative Chaotic Quantum Maps
- Semiclassics for a Dissipative Quantum Map
- Corner transfer matrices for 2D strongly coupled many-body Floquet systems
- Algebraic decay in hierarchical graphs
- A Farewell to Liouvillians
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- Lieb-Schultz-Mattis Theorem in Open Quantum Systems
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- Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
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- Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
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- 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
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- Field theory of non-Hermitian disordered systems
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- Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
- Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
- Stochastic Operator Variance: an observable to diagnose noise and scrambling
- Multifractality of many-body non-Hermitian skin effect
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- Theory of Irreversibility in Quantum Many-Body Systems
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- Non-equilibrium boundary driven quantum systems: models, methods and properties
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- Localization of Lindbladian Fermions
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