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arXiv · 2208.09306

Bifurcation and anomalous spectral accumulation in oval billiard

Hironori Makino
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Abstract

Spectral statistics of quantum oval billiard whose classical dynamical system shows bifurcations is numerically investigated in terms of the two-point correlation function (TPCF) which is defined as the probability density of finding two levels at a specific energy interval. The eigenenergy levels at bifurcation point is found to show anomalous accumulation which is observed as a periodic spike oscillation of the TPCF. We analyzed the eigenfunctions localizing onto the various classical trajectories in the phase space and found that the oscillation is supplied from a limited region in the phase space, which contains the bifurcating orbit. We also show that the period of the oscillation is in good agreement with the period of a contribution from the bifurcating orbit to the semiclassical TPCF obtained by Gutzwiller trace formula.

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Hironori Makino. 2022-08-19. Bifurcation and anomalous spectral accumulation in oval billiard. https://doi.org/10.1093/ptep/ptz077

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