The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.
In this paper, we add a supplementary contribution and support to the path integral method by exploring the theory of radiation in plasma physics. This method, based on the Feynman path integral formalism, has the advantage of treating the electrons and ions on the same physical basis and both time-independent and time-dependent problems on the same footing. Since the main quantity in the problem of plasma radiation is the dipolar autocorrelation function of the radiator, we derive it using the path integral technique in its perturbative form. We show that the dipolar autocorrelation function could be written as a generalized expression taking into account the time-dependency effects.
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