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Research Article Open access CC BY 4.0

Application of Fractional Classical and Quantum Mechanics to Statistical Physics System

Z. Korichi, M. T. Meftah

Physical Science International Journal · pp. 1–13 · Published 8 Sep 2015

10.9734/PSIJ/2015/20366

Abstract

In this work, we focus our study on some systems in statistical mechanics by using a recent developpment of the fractional classical and quantum mechanics. At first, we present the thermodynamical properties of N classical and quantum oscillators in 3-dimensional space. In each case, the Hamiltonian, describing the system, exhibits fractional powers. Secondly, in the context of the fractional quantum mechanics, we calculate the thermodynamical properties for the systems: the trapped ideal Bose and Fermi gases. For the trapped ideal Bose system, Bose- Einstein condensation and the thermodynamics properties are discussed and plotted with respect to the fractional powers and the temperature. It is shown that the trapped ideal Bose gas exhibits a phase transition at a temperature TC for which the specific heat presents a discontinuity depending on the fractional powers. All calculations are performed in 3-dimensional space.

Fractional classical mechanics fractional quantum mechanics Partition function Thermo- dynamics properties Oscillators system Bose system Bose-Einstein condensation

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