arXiv subjects

M. Batsch

Publications and source records attributed to M. Batsch.

6 recordsLinked to original sources

arXiv1997

Phase diagram of localization in a magnetic field

The phase diagram of localization is numerically calculated for a three-dimensional disordered system in the presence of a magnetic field using the Peierls substitution. The mobility edge trajectory shifts in the energy-disorder space when increasing the field. In the band center, localized states near the phase boundary become delocalized. The obtained field dependence of the critical disorder is in agreement with a power law behavior expected from scaling theory. Close to the tail of the band the magnetic field causes localization of extended states.

cond-mat.dis-nn↗

arXiv1997

Energy-level statistics and localization of 2d electrons in random magnetic fields

Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this model, extended states have recently been proposed to exist in the middle of the band. In contrast, from our calculations of the large-$s$ behavior of the nearest neighbor level spacing distribution $P(s)$ and from a finite size scaling analysis we find only localized states in the suggested energy and disorder range.

cond-mat.mes-hall↗

arXiv1996

Level statistics in the quantum Hall regime

The statistical properties of energy eigenvalues in the critical regime of the lowest Landau band are investigated. The nearest neighbour level spacing distribution $P(s)$ and the Mehta quantity $I_0$, from which the scaling exponent $ν$ of the correlation length can be derived, are calculated. While $P(s)$ disagrees with recent analytical predictions, $ν$ is found to be in agreement with theoretical and experimental results.

cond-mat↗

arXiv1996

Crossover from critical orthogonal to critical unitary statistics at the Anderson transition

We report a novel scale-independent, Aharonov-Bohm flux controlled crossover from critical orthogonal to critical unitary statistics at the disorder induced metal insulator transition. Our numerical investigations show that at the critical point the level statistics are definitely distinct and determined by fundamental symmetries. The latter is similar to the behavior of the metallic phase known from random matrix theory. The Aharonov-Bohm flux dependent crossover is characteristic of the critical ensemble.

cond-mat↗

arXiv1996

Mean-field limit of the random flux model

The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the problem onto Wegner's $N$-orbital model in the same limit, while the original problem corresponds to $N=1$. The exact solution for $N=\infty$, the mean--field limit, is discussed and compared with numerical results. An outline of a $1/N$-expansion is given.

cond-mat↗

arXiv1996

Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions

We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system sizes up to 1024 $\times$ 1024 lattice sites exhibits a crossover between Wigner and Poisson distributions. We perform a self-contained finite-size scaling analysis to find a single-valued one-parameter function $γ(L/ξ)$ which governs the crossover. The scaling parameter $ξ(W)$ is deduced and compared with the localization length. $γ( L/ξ)$ does {\em not} show critical behavior and has two asymptotic regimes corresponding to weakly and strongly localized states.

cond-mat↗