Regensburg 1998 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 18: POSTER I
DY 18.35: Poster
Montag, 23. März 1998, 14:30–17:30, D
Universal parametric correlations in complex quantum systems — •Ville Uski1, B. Mehlig2, R. A. Römer1, and M. Schreiber1 — 1Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz — 2Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden
We calculate correlation functions for the statistical fluctuations of smoothed spectral densities in complex quantum systems. We derive formulas for the correlations within the semi-classical approximation, where the fluctuations are written as sums over classical periodic orbits. We compare the obtained expressions with our numerical results from the Anderson model of localisation. We use the magnetic flux φ as external parameter and analyse the transition from the Gaussian orthogonal ensemble at φ=0 to the Gaussian unitary ensemble at finite φ. We also calculate fluctuations at two values of φ and analyse the statistics as a function of the difference. We obtain results for the density of states, for the density of level velocities and for the density of matrix elements of the position operator. For the values of smoothing parameter close to the mean level spacing the semi-classical expressions and the numerical results agree quite well in the whole range of the magnetic flux.