2013/02/28 by Benjamin Batistić, Batistić, Benjamin, Marko Robnik +1 · 1 citation
Physics and Astronomy · #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Opinion Dynamics and Social Influence
paper · pdf · doi:10.48550/arxiv.1302.7174
We study the quantum mechanics of a billiard (Robnik 1983) in the regime of\nmixed-type classical phase space (the shape parameter \λ=0.15) at very\nhigh-lying eigenstates, starting at about 1.000.000th eigenstate and including\nthe consecutive 587654 eigenstates. By calculating the normalized Poincar 'e\nHusimi functions of the eigenstates and comparing them with the classical phase\nspace structure, we introduce the overlap criterion which enables us to\nseparate with great accuracy and reliability the regular and chaotic\neigenstates, and the corresponding energies. The chaotic eigenstates appear all\nto be dynamically localized, meaning that they do not occupy unformly the\nentire available chaotic classical phase space component, but are localized on\na proper subset. We find with unprecedented precision and statistical\nsignificance that the level spacing distribution of the regular levels obeys\nthe Poisson statistics, and the chaotic ones obey the Brody statistics, as\nanticipated in a recent paper by Batisti 'c and Robnik (2010), where the entire\nspectrum was found to obey the BRB statistics. There are no effects of\ndynamical tunneling in this regime, due to the high energies, as they decay\nexponentially with the inverse effective Planck constant which is proportional\nto the square root of the energy.\n