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Classical Resonances and Quantum Scarring

Christopher Manderfeld
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Abstract

We study the correspondence between phase-space localization of quantum (quasi-)energy eigenstates and classical correlation decay, given by Ruelle-Pollicott resonances of the Frobenius-Perron operator. It will be shown that scarred (quasi-)energy eigenstates are correlated: Pairs of eigenstates strongly overlap in phase space (scar in same phase-space regions) if the difference of their eigenenergies is close to the phase of a leading classical resonance. Phase-space localization of quantum states will be measured by $L^2$ norms of their Husimi functions.

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Christopher Manderfeld. 2003-01-22. Classical Resonances and Quantum Scarring. https://arxiv.org/abs/nlin/0301028

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