Search results for "Level-spacing distribution"
showing 4 items of 4 documents
Universality of level spacing distributions in classical chaos
2007
Abstract We suggest that random matrix theory applied to a matrix of lengths of classical trajectories can be used in classical billiards to distinguish chaotic from non-chaotic behavior. We consider in 2D the integrable circular and rectangular billiard, the chaotic cardioid, Sinai and stadium billiard as well as mixed billiards from the Limacon/Robnik family. From the spectrum of the length matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe non-generic (Dirac comb) behavior in the integrable case and Wignerian behavior in the chaotic case. For the Robnik billiard close to the circle the distribution approaches a Poissonian dis…
Shape analysis of the level-spacing distribution around the metal-insulator transition in the three-dimensional Anderson model
1995
We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.…
Level-spacing distribution in the tight-binding model of fcc clusters.
1993
A lattice-gas Monte Carlo method is used to simulate metallic fcc clusters at finite temperatures. A tight-binding model including s and p electrons has been derived for reproducing the free-electron-like energy band for the bulk metal and this model is used for calculating the electronic structures of the fcc cluster. The resulting level-spacing distribution at the Fermi energy is a Wigner distribution. The width of the distribution in small clusters is smaller than that calculated from the bulk density of states. In the lattice gas clusters the energy gaps related to the electronic magic numbers do not show up at the Fermi level. The energy between the last occupied and the first unoccupi…
Shell structure and level spacing distribution in metallic clusters
1993
The lattice gas Monte Carlo and tight binding method is used to study the electronic shell structure in large metallic clusters. The average density of states of a large ensemble of deformed clusters shows the same shell structure as the most spherical geometry. The level spacing distribution at the Fermi level is a Wigner distribution.