0000000000037596
AUTHOR
E. Hofstetter
Statistical properties of the eigenvalue spectrum of the three-dimensional Anderson Hamiltonian
A method to describe the metal-insulator transition (MIT) in disordered systems is presented. For this purpose the statistical properties of the eigenvalue spectrum of the Anderson Hamiltonian are considered. As the MIT corresponds to the transition between chaotic and nonchaotic behavior, it can be expected that the random matrix theory enables a qualitative description of the phase transition. We show that it is possible to determine the critical disorder in this way. In the thermodynamic limit the critical point behavior separates two different regimes: one for the metallic side and one for the insulating side.
Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model
A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.
Shape analysis of the level-spacing distribution around the metal-insulator transition in the three-dimensional Anderson model
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.…
Band Tails in a Disordered System
In crystalline solids electronic excitations have a band structure. Energy intervals, in which excitations occur, are separated by band gaps, where the density of electronic states vanishes. At the band edge the density-of-states (DOS) has power law singularities, so-called van Hove singularities.