Spectral Gaps and Midgap States in Random Quantum Master Equations.

  title={Spectral Gaps and Midgap States in Random Quantum Master Equations.},
  author={Tankut Can and Vadim Oganesyan and Dror Orgad and Sarang Gopalakrishnan},
  journal={Physical review letters},
  volume={123 23},
We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random N×N Hermitian matrices, and study the spectral properties of the resulting Liouvillian superoperator. We consider various random-matrix ensembles, and find that for all of them the asymptotic decay rate remains nonzero in the thermodynamic limit; i.e., the spectrum of the superoperator is gapped as N→∞. For finite N, the probability of finding a very… 

Figures from this paper

Dissipation and decoherence for generic open quantum systems
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
Spectral transitions and universal steady states in random Kraus maps and circuits
The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question
Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos.
It is shown that DSFF successfully diagnoses dissipative quantum chaos and reveals correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy scale (and timescale), and that the DSFF takes a constant value except for a region in complex time whose size and behavior depend on the eigenvalue density.
Full Spectrum of the Liouvillian of Open Dissipative Quantum Systems in the Zeno Limit.
This work derives effective LME equations describing the modes within each stripe separately, and solves them perturbatively, obtaining the full set of eigenvalues and eigenstates of the Liouvillian explicit expressions correct at order 1/Γ included, where Γ is the strength of the dissipation.
Spectral and steady-state properties of random Liouvillians
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
Entanglement in nonequilibrium steady states and many-body localization breakdown in a current-driven system
We model a one-dimensional (1D) current-driven interacting disordered system through a non-Hermitian Hamiltonian with asymmetric hopping and study the entanglement properties of its eigenstates. In
Non-stationarity and dissipative time crystals: spectral properties and finite-size effects
We discuss the emergence of non-stationarity in open quantum many-body systems. This leads us to the definition of dissipative time crystals which display experimentally observable, persistent,
Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral
Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of
Hierarchy of Relaxation Timescales in Local Random Liouvillians.
This work analyzes a spin-1/2 system of size ℓ with up to n-body Lindblad operators, which are n local in the complexity-theory sense, and finds that the positivity of the map implies a sharp separation of the relaxation timescales according to the locality of observables.


Relaxation times of dissipative many-body quantum systems.
  • M. Znidaric
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system
Power-law approach to steady state in open lattices of noninteracting electrons
We address the question of how a non-equilibrium steady state (NESS) is reached in the Linbdladian dynamics of an open quantum system. We develop an expansion of the density matrix in terms of the
Controlling the dynamics of an open many-body quantum system with localized dissipation.
The link between the dissipative dynamics and the measurement of the density distribution of the BEC allowing for a generalized definition of the Zeno effect is demonstrated.
Fluctuation-Induced Quantum Zeno Effect.
This work investigates the effect of a local dissipative impurity on a one-dimensional gas of interacting fermions and shows that the escape probability for modes close to the Fermi energy vanishes for an arbitrary strength of the dissipation.
Spectral theory of Liouvillians for dissipative phase transitions
A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both
Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems.
Investigation of spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group finds that the decoherence time diverges in the thermodynamic limit, and the coherence decay is then algebraic instead of exponential.
Random-matrix theory of quantum transport
This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined
Matrix product simulations of non-equilibrium steady states of quantum spin chains
A time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable
Thouless and relaxation time scales in many-body quantum systems
A major open question in studies of nonequilibrium quantum dynamics is the identification of the time scales involved in the relaxation process of isolated quantum systems that have many interacting