Adiabatic Invariants and Some Statistical Properties of the Time Dependent Linear and Nonlinear Oscillators

Robnik, Marko

doi:10.1007/978-3-319-27635-9_4

Cited by 1 publication

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“…, where the weight ρ ∈ [0, 1] is assumed to coincide with the relative phase volume(Liouvillé measure) of the chaotic component in the classical dynamical system having a single chaotic region [5]. In this paper we do not go into its physical meaning and deal with ρ as a parameter.…”

Section: Effect Of Bifurcation On Energy Level Statisticsmentioning

confidence: 99%

“…In between these two extremes is a generic case of mixed type dynamics where regular and chaotic orbits coexist in the classical phase space. In this case, it has been proposed that the quantum level statistics is a combination of the Poisson and GOE/GUE statistics [3,4], with relative weights determined by the corresponding phase volumes (Liouville measures) of the regular and chaotic orbits [5].…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation and anomalous spectral accumulation in an oval billiard

Makino¹

2019

Progress of Theoretical and Experimental Physics

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The spectral statistics of a 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 the bifurcation point are 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 that 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’s trace formula [J. Math. Phys. 12, 343 (1971)].

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Section: Effect Of Bifurcation On Energy Level Statisticsmentioning

confidence: 99%