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DY: Dynamik und Statistische Physik

DY 50: Quantum chaos I

DY 50.2: Vortrag

Freitag, 28. März 2003, 10:30–10:45, G\"OR/226

Analysis of level statistics and eigenfunctions of pseudointegrable systems — •Yuriy Hlushchuk und Stefanie Russ — Institut fuer Theoretische Physik III, Heinrich-Buff-Ring 16, D-35392 Giessen

We study the level statistics (second half moment I₀ and rigidity Δ₃) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers g. We find that the levels form energy intervals with a characteristic behavior of the level statistics and the eigenfunctions in each interval. At low enough energies, the boundary roughness is not resolved and accordingly, the eigenfunctions are quite regular functions and the level statistics shows Poisson-like behavior. At higher energies, the level statistics of most systems moves from Poisson-like towards Wigner-like behavior with increasing g.

Investigating the wavefunctions, we find many chaotic functions that can be described as a random superposition of regular wavefunctions. The amplitude distribution P(ψ) of these chaotic functions was found to be Gaussian with the typical value of the localization volume V_loc≈ 0.33.

For systems with periodic boundaries we find several additional energy regimes, where I₀ is relatively close to the Poisson-limit. In these regimes, the eigenfunctions are either regular or localized functions, where P(ψ) is close to the distribution of a sine or cosine function in the first case and strongly peaked in the second case. Also an interesting intermediate case between chaotic and localized eigenfunctions appears.