Fractional approach, quantum statistics, and non-crystalline solids at very low temperatures
Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá Paraná, Brazil
Corresponding author: a firstname.lastname@example.org
Revised: 5 March 2008
Published online: 11 April 2008
We consider nonlocal effects, obtained by incorporating fractional derivatives in the kinetic energy of a conventional Hamiltonian, to analyze physical properties of non-crystalline solids at very low temperature. By using thermal Green functions, we deduce some experimentally observable quantities such as the particle momentum distribution function, the particle energy distribution function, and the specific heat. The agreement between the results obtained for the specific heat and the experimental data suggests that the approach presented here may be useful as a phenomenological model to investigate thermal properties of non-crystalline solids at low temperature.
PACS: 05.30.-d – Quantum statistical mechanics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008