Critical Level-Spacing Distribution for General Boundary Conditions

Abstract

It is believed that the semi-Poisson function $P(S)=4S\exp (-2S)$ describes the normalized distribution of the nearest level-spacings $S$ for critical energy levels at the Anderson metal-insulator transition from quantum chaos to integrability, after an average over four obvious boundary conditions (BC) is taken (Braun {\it et} {\it al} \cite{1}). In order to check whether the semi-Poisson is the correct universal distribution at criticality we numerically compute it by integrating over all possible boundary conditions. We find that although $P(S)$ describes very well the main part of the obtained critical distribution small differences exist particularly in the large $S$ tail. The simpler crossover between the integrable ballistic and localized limits is shown to be universally characterized by a Gaussian-like $P(S)$ distribution instead.

4 pages and 3 figures

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• The Statistical Theory of Quantum Dots
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Cited by in corpus (3)

• Numerical simulation of the localization of elastic waves in two- and three-dimensional heterogeneous media
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• Boundary hopping and the mobility edge in the Anderson model in three dimensions