Sven Gnutzmann

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We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2D quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic underlying classical dynamics, and for each case the limiting distribution is universal (system independent). Thus, a new(More)
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear -model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner-Dyson random(More)
Sequences of nodal counts store information on the geometry (metric) of the domain where the wave equation is considered. To demonstrate this statement, we consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of revolution. Arranging the wave functions by increasing values of the eigenvalues, and counting the number of their nodal(More)
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter-the ratio ρ between the area of a domain and its perimeter, measured in units of the wavelength 1/ √ E. We show that the distribution function P (ρ) can distinguish between domains in which the classical dynamics is regular(More)