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Correlation structure of the deltan statistic for chaotic quantum systems
A Relaño1, J Retamosa, E Faleiro
1Departamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de Madrid, 28040 Madrid, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
Quantum energy spectra analyzed as time series reveal chaotic systems exhibit noise, unlike regular systems. A height-height correlation function shows logarithmic behavior in chaotic spectra, similar to random phase time series.
Area of Science:
- Quantum mechanics
- Statistical physics
- Time series analysis
Background:
- A formal analogy exists between quantum energy spectra and discrete time series.
- The statistic characterizes energy level fluctuations, distinguishing chaotic systems (noise) from regular systems.
Purpose of the Study:
- Investigate the correlation structure of the statistic.
- Analyze the height-height correlation function for quantum chaotic systems and noise time series.
Main Methods:
- Studied the -order height-height correlation function.
- Modeled chaotic quantum systems using random matrix theory.
- Generated time series as linear combinations of cosine functions with random phases.
Main Results:
- The height-height correlation function exhibits logarithmic behavior for chaotic quantum spectra.
- This logarithmic behavior was accurately reproduced in time series generated with random phases.
Conclusions:
- The height-height correlation function provides insights into the nature of quantum chaotic systems.
- The study establishes a connection between quantum chaos and the properties of time series with noise.