# Universal Spectra of Random Lindblad Operators.

@article{Denisov2019UniversalSO, title={Universal Spectra of Random Lindblad Operators.}, author={Sergey V. Denisov and Tetyana Laptyeva and Wojciech Tarnowski and Dariusz Chruściński and Karol Życzkowski}, journal={Physical review letters}, year={2019}, volume={123 14}, pages={ 140403 } }

To understand the typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate completely positive Markovian evolution in the space of the density matrices. The spectral properties of these operators, including the shape of the eigenvalue distribution in the complex plane, are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models. We also demonstrate the universality of the…

## 32 Citations

Random-matrix theory for the Lindblad master equation.

- PhysicsChaos
- 2021

Random-matrix theory is applied to the Lindblad superoperator to elucidate its spectral properties and the distribution of eigenvalues and the correlations of neighboring eigen values are obtained for the cases of purely unitary dynamics, pure dissipation, and the physically realistic combination of unitary and dissipative dynamics.

From integrability to chaos in quantum Liouvillians

- MathematicsSciPost Physics Core
- 2022

The dynamics of open quantum systems can be described by a Liouvillian, which in the Markovian approximation fulfills the Lindblad master equation. We present a family of integrable many-body…

Spectral transitions and universal steady states in random Kraus maps and circuits

- PhysicsPhysical Review B
- 2020

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…

Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems.

- PhysicsPhysical review letters
- 2019

We study the transition between integrable and chaotic behavior in dissipative open quantum systems, exemplified by a boundary driven quantum spin chain. The repulsion between the complex eigenvalues…

Random generators of Markovian evolution: A quantum-classical transition by superdecoherence.

- PhysicsPhysical review. E
- 2021

An inverse procedure of supercoherification is defined that is a generalization of the scheme used to construct a quantum state out of a classical one and observes a sharp quantum-to-classical transition.

Spectral and steady-state properties of random Liouvillians

- Mathematics, PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

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 Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos.

- PhysicsPhysical review letters
- 2021

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.

Spectral Gaps and Midgap States in Random Quantum Master Equations.

- PhysicsPhysical review letters
- 2019

It is given evidence that midgap states exist also for nonrandom system-noise coupling and discuss some experimental implications of the above results.

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

- Physics
- 2019

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…

A non-Hermitian PT-symmetric kicked top

- PhysicsNew Journal of Physics
- 2020

A non-Hermitian PT-symmetric version of the kicked top is introduced to study the interplay of quantum chaos with balanced loss and gain. The classical dynamics arising from the quantum dynamics of…

## References

SHOWING 1-10 OF 83 REFERENCES

Universality of spectra for interacting quantum chaotic systems.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

A model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements, shows that the spectra of the evolution operator exhibit an universal behavior and can be described by an ensemble of real random Ginibre matrices.

Detecting Non-Markovianity of Quantum Evolution via Spectra of Dynamical Maps.

- Mathematics, PhysicsPhysical review letters
- 2017

The dynamical analog of entanglement witness is introduced to detect non-Markovianity and it is shown that for several important classes of dynamical maps the corresponding evolution of singular values and/or eigenvalues of the map provides a simple non- MARKOVianity witness.

Spectral and steady-state properties of random Liouvillians

- Mathematics, PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

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…

Random Lindblad equations from complex environments.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

It is demonstrated that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir and the anomalous irreversible behavior of a quantum tunneling system described in an effective two-level approximation.

Generating random density matrices

- Mathematics
- 2010

We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states,…

Quantum Dynamical Semigroups and Applications

- Physics
- 1987

In this text the authors develop quantum dynamics of open systems for a wide class of irreversible processes starting from the concept of completely positive semigroups. This unified approach makes…

On the generators of quantum dynamical semigroups

- Mathematics
- 1976

The notion of a quantum dynamical semigroup is defined using the concept of a completely positive map. An explicit form of a bounded generator of such a semigroup onB(ℋ) is derived. This is a quantum…

Random transition-rate matrices for the master equation.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic…