Connection Between Quantum-Classical Correspondence and Long-Range Correlations in Quantum Spectra
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Abstract
Based on the Berry-Tabor trace formula, a semiclassical quantization condition for the periodic orbits in a two-dimensional uncoupled oscillator system and the correspondence relation between the quantum levels and classical trajectories of the system have been studied in detail. Making use of the quantum-classical correspondence relation, it has been found that if a set of quantum levels corresponds to the periodic orbits with the same topology structure M (M1,M2), there will be long-range correlations among these quantum levels.
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