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Universal Spectra of Random Lindblad Operators.
Sergey Denisov1,2, Tetyana Laptyeva2, Wojciech Tarnowski3
1Department of Computer Science, OsloMet-Oslo Metropolitan University, NO-0130 Oslo, Norway.
Physical Review Letters
|November 9, 2019
Summary
We introduce random Lindblad operators to model open quantum systems. This approach helps categorize quantum chaos by analyzing spectral properties and eigenvalue distributions.
Area of Science:
- Quantum Physics
- Quantum Information Theory
- Statistical Mechanics
Background:
- Understanding open quantum systems is crucial for quantum technologies.
- Markovian evolution describes systems losing quantum coherence over time.
- Dissipative quantum chaos is an emerging field requiring new theoretical tools.
Purpose of the Study:
- To develop a theoretical framework for analyzing the dynamics of open quantum systems.
- To investigate the spectral properties of random Lindblad operators.
- To establish a connection between random matrix theory and quantum chaos.
Main Methods:
- Introducing an ensemble of random Lindblad operators.
- Applying methods of free probability theory.
- Utilizing non-Hermitian random matrix models.
Main Results:
- Demonstrated that random Lindblad operators generate completely positive Markovian evolution.
- Characterized the spectral properties, including eigenvalue distribution.
- Showcased the universality of observed spectral features.
Conclusions:
- The ensemble of random generators provides a novel approach to studying Markovian quantum evolution.
- This work offers a step towards categorizing dissipative quantum chaos.
- The findings have implications for understanding decoherence and quantum information processing.
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