In this work, we study the Anderson-Falicov-Kimball model within the dynamical mean field theory for the Bethe lattice, restricting our analysis to the nonmagnetic case. The one-particle density of states is obtained by both arithmetic and geometric averages over disorder, since only the latter can detect localization in the absence of an energy gap. Varying the strengths of Coulomb interaction and disorder at zero temperature, we construct phase diagrams for this model, where we distinguish spectral regions with localized states, with extended states, or with a correlation-induced gap. With this, we identify metal-insulator transitions driven by correlation and disorder, as well as the competition between these effects. This is done for various band fillings, since our main interest here is to study how the variation of the electron density affects the phase diagrams previously obtained for half-filling. The picture revealed by the density of states is further checked by evaluating the static and dynamic conductivities, including temperature effects.
The role of Coulomb disorder is analysed in the Anderson-Falicov-Kimball model. Phase diagrams of correlated and disordered electron systems are calculated within dynamical mean-field theory applied to the Bethe lattice, in which metal-insulator transitions led by structural and Coulomb disorders and correlation can be identified. Metallic, Mott insulator, and Anderson insulator phases, as well as the crossover between them are studied in this perspective. We show that Coulomb disorder has a relevant role in the phase-transition behavior as the system is led towards the insulator regime.
We investigate the stability of "magnetic" ordering against band-filling changes and Anderson-like disorder in the Falicov-Kimball model, within dynamical mean-field theory (DMFT). The one-particle density of states is obtained by both arithmetic and geometric averages over disorder, allowing us to detect the localization transition. Varying the Coulomb interaction and disorder strength, we construct phase diagrams where we identify metallic and insulating regions, with or without magnetic ordering, and determine how these phases are affected by band filling.
Classical systems of coupled harmonic oscillators are studied using the Carati-Galgani model. We investigate the consequences for Einstein's conjecture by considering that the exchanges of energy, in molecular collisions, follows the Lévy type statistics. We develop a generalization of Planck's distribution admitting that there are analogous relations in the equilibrium quantum statistical mechanics of the relations found using the nonequilibrium classical statistical mechanics approach. The generalization of Planck's law based on the nonextensive statistical mechanics formalism is compatible with the our analysis.
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