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Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems
Roman Riser1, Vladimir Al Osipov2, Eugene Kanzieper1
1Department of Applied Mathematics, H.I.T.-Holon Institute of Technology, Holon 5810201, Israel.
Physical Review Letters
|June 6, 2017
Summary
We present a universal prediction for energy level fluctuation power spectra in chaotic quantum systems with broken time-reversal symmetry, challenging traditional assumptions about spectral properties.
Area of Science:
- Quantum Chaos
- Statistical Mechanics
- Random Matrix Theory
Background:
- Understanding energy level fluctuations is key in quantum chaos.
- Time-reversal symmetry breaking is a crucial factor in spectral properties.
- Previous models often relied on the spectral form factor.
Purpose of the Study:
- To provide a nonperturbative analysis of the power spectrum of energy level fluctuations.
- To derive a universal prediction for systems with broken time-reversal symmetry.
- To challenge the assumption that the power spectrum is solely determined by the spectral form factor.
Main Methods:
- Utilized finite-N random matrix theory.
- Derived an exact multidimensional integral representation for the power spectrum.
- Analyzed the N→∞ limit of the derived solution.
Main Results:
- Obtained a universal, parameter-free prediction for the power spectrum.
- Expressed the prediction in terms of a fifth Painlevé transcendent.
- Validated the theoretical predictions through extensive numerical simulations.
Conclusions:
- The study invalidates the traditional assumption linking power spectrum solely to the spectral form factor.
- The derived universal prediction offers new insights into quantum chaotic systems.
- The findings highlight the importance of nonperturbative methods in quantum chaos analysis.
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