R. Rossato

Time dependent solutions for a fractional Schrödinger equation with delta potentials

We investigate, for an arbitrary initial condition, the time dependent solutions for a fractional Schrodinger equation in the presence of delta potentials by using the Green function approach. The solutions obtained show an anomalous spreading asymptotically characterized by a power-law behavior, which is governed by the order of the fractional spatial operator present in the Schrodinger equation.

Nonlocal effects on the thermal behavior of non-crystalline solids

We argue that nonlocal effects represented by fractionary terms in the kinetic energy can be relevant to achieve a satisfactory phenomenological description of the thermal behavior of the specific heat of non-crystalline solids at very low temperature. We propose a simple model formed by the direct sum of two Hamiltonians, one of which is obtained by incorporating fractional derivatives in the kinetic energy of a conventional Hamiltonian, and the other one accounts for the presence of phonons in the system. Some experimental data are used to support the proposed description.