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Parametric number covariance in quantum chaotic spectra
Vinayak1, Sandeep Kumar1,2, Akhilesh Pandey1
1School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
Physical Review. E
|April 15, 2016
Summary
We introduce number covariance to measure spectral correlations in quantum chaotic systems. This new measure shows universality across different quantum systems, offering insights into their behavior.
Area of Science:
- Quantum chaos
- Statistical quantum mechanics
- Quantum information
Background:
- Spectral correlations are crucial for understanding quantum chaotic systems.
- Existing measures may not fully capture parametric correlations.
- Random matrix theory provides a framework for studying spectral statistics.
Purpose of the Study:
- Introduce and define number covariance as a novel measure for spectral parametric correlations.
- Derive analytic results for number covariance in classical random matrix ensembles.
- Investigate the universality of number covariance in quantum chaotic systems.
Main Methods:
- Utilized the binary correlation method for analytic derivations.
- Applied spectral analysis to quantum kicked rotor models.
- Examined both time-reversal invariant and noninvariant cases.
Main Results:
- Derived compact analytic expressions for number covariance.
- Demonstrated the universality of number covariance through analysis of quantum kicked rotors.
- Investigated a local version of parametric number variance.
Conclusions:
- Number covariance is a robust and universal measure of spectral parametric correlations.
- The findings provide new tools for analyzing quantum chaotic systems.
- This work contributes to the understanding of statistical properties in quantum mechanics.
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