Crossover of level statistics between strong and weak localization in two dimensions
I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstrasse
9, D-20355 Hamburg, Germany
2 Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany
Accepted: 18 April 1996
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 the spacings calculated for system size up to 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 which governs the crossover. The scaling parameter is deduced and compared with the localization length. does not show critical behaviour and has two asymptotic regimes corresponding to weakly and strongly localized states.
PACS: 71.55.Jv – Disordered structures; amorphous and glassy solids / 72.15.Rn – Quantum localization / 05.45.+b – Theory and models of chaotic systems
© EDP Sciences, 1996