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Eigenvalue statistics as an indicator of integrability of nonequilibrium density operators
1Department of Physics, FMF, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.
Physical Review Letters
|October 8, 2013
Summary
We propose using eigenvalue statistics to quantify quantum system complexity. Poissonian statistics indicate integrability, while random matrix statistics suggest nonintegrability in quantum nonequilibrium systems.
Area of Science:
- Quantum physics
- Statistical mechanics
- Complex systems
Background:
- Quantifying complexity in quantum systems is crucial for understanding their behavior.
- Nonequilibrium steady states and long-lived decay modes present unique challenges in complexity analysis.
Purpose of the Study:
- To develop a method for quantifying the complexity of quantum nonequilibrium steady state density operators.
- To analyze long-lived Liouvillian decay modes using spectral properties.
Main Methods:
- Analyzing the level spacing distribution of spectra for density operators and Liouvillian decay modes.
- Conducting extensive numerical studies across various quantum models.
Main Results:
- A conjecture linking integrability to Poissonian level statistics.
- Identification of Gaussian unitary ensemble statistics in generic nonintegrable systems.
- Demonstration of eigenvalue statistics as a tool for identifying integrable quantum systems.
Conclusions:
- Level spacing distribution serves as an effective indicator of integrability in quantum systems.
- Eigenvalue statistics provide an efficient method for classifying quantum nonequilibrium systems.
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