Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons

We investigate the shape of the spectrum and the spectral fluctuations of the $k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the number of Bosons $m \to \infty$ while both $k$, the rank of the interaction, and $l$, the number of single-particle states, are kept fixed. We show that the relative fluctuations of the low spectral moments do not vanish in this limit, proving that the ensemble is non-ergodic. Numerical simulations yield spectra which display a strong tendency towards picket-fence type. The wave functions also deviate from canonical random-matrix behaviourComment: 7 pages, 5 figures, uses epl.cls (included

Cross-Section Fluctuations in Chaotic Scattering

For the theoretical prediction of cross-section fluctuations in chaotic scattering, the cross-section autocorrelation function is needed. That function is not known analytically. Using experimental data and numerical simulations, we show that an analytical approximation to the cross-section autocorrelation function can be obtained with the help of expressions first derived by Davis and Boose. Given the values of the average S-matrix elements and the mean level density of the scattering system, one can then reliably predict cross-section fluctuations

Information about the Integer Quantum Hall Transition Extracted from the Autocorrelation Function of Spectral Determinants

The Autocorrelation function of spectral determinants (ASD) is used to probe the sensitivity of a two-dimensional disordered electron gas to the system's size L. For weak magnetic fields ASD is shown to depend only trivially on L, which is a strong indication that all states are localized. From nontrivial dependence of ASD on L for infinite L at a Hall conductance of 1/2 e^2/h we deduce the existence of critical wave functions at this point, as long as the disorder strength does not exceed a critical value.Comment: 4 pages, one citation correcte

Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical formula for the localisation length is derived, describing the dimensional crossover as function of width $L_y$, conductance $g$ and perpendicular magnetic field $B$ . On the basis of these results, the scaling analysis of the quantum Hall effect in high Landau levels, and the delocalisation transition in a quantum Hall wire are reconsidered.Comment: 12 pages, 7 figure