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DY: Dynamik und Statistische Physik

DY 25: Quantenchaos I

DY 25.2: Vortrag

Dienstag, 12. März 2002, 14:45–15:00, H3

Pseudointegrable systems with growing roughness in the low and high energy limits — •Yuriy Hlushchuk and Stefanie Russ — Institut fuer Theoretische Physik, Universitaet Giessen, Heinrich-Buff-Ring 16, 35392 Giessen

We studied the level statistics in the spectra of pseudointegrable billards with different genus numbers g and in particular the second half moments I₀ = ⟨ s² ⟩/2, where s is the normalized distance between two consecutive eigenvalues. For comparatively high energy an asymptotic regime was found. In that regime I₀ seems to depend only on g and to approach the Wigner limit I₀ ≈ 0.637 with increasing surface roughness, i.e., with increasing g. In the low energy range several windows with larger I₀-values, closer to the Poisson-limit of I₀ = 1 were found. The size and position of the windows depended on the shape of the billard. In order to understand the origin of such behavior the eigenfunctions were calculated and their amplitude distributions P(Ψ) and localization volumes V_loc were studied. These calculations showed the existence of either localized or regular functions in such regimes, whereas chaotic functions dominate the asymptotic regime. Very good agreement between parameters describing the eigenfunctions and values of I₀ was observed.