Application of Fractional Classical and Quantum Mechanics to Statistical Physics System
Z. Korichi
Department of Physics, Faculty of Mathematics and Matter Physics, LRPPS Laboratory, University UKMO Ouargla, 30000, Algeria
M. T. Meftah *
Department of Physics, Faculty of Mathematics and Matter Physics, LRPPS Laboratory, University UKMO Ouargla, 30000, Algeria
*Author to whom correspondence should be addressed.
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.
Keywords: Fractional classical mechanics, fractional quantum mechanics, Partition function, Thermo- dynamics properties, Oscillators system, Bose system, Bose-Einstein condensation