Exploring classical phase space structures of nearly integrable and mixed quantum systems via parametric variation

Area of Science:

• Quantum mechanics
• Statistical physics
• Chaos theory

Background:

• Phase space localization is a key concept in quantum systems.
• Previous studies focused on chaotic quantum systems.
• A sensitive measure involving overlap intensities and level velocities was developed.

Purpose of the Study:

• To extend the theory of phase space localization to near-integrable and mixed quantum systems.
• To investigate the utility of the overlap intensity-level velocity correlation in these systems.
• To explore the applicability of Hannay-Ozorio de Almeida sum rules in mixed phase space systems.

Main Methods:

• Development of a detailed semiclassical theory.
• Relating the correlation coefficient to phase space weighted derivatives of the classical action.
• Derivation of Planck's over 2pi scalings for nearly integrable systems.

Main Results:

• The correlation measure effectively highlights phase space structures in mixed quantum systems.
• The theory shows excellent agreement with results from integrable billiards and the standard map.
• The study addresses the extendibility of sum rules to mixed phase space systems.

Conclusions:

• The developed theory provides a sensitive tool for analyzing phase space localization in a broader range of quantum systems.
• The correlation measure is particularly useful for understanding perturbation-dependent structures in mixed systems.
• The findings contribute to the understanding of quantum-classical correspondence in non-chaotic systems.