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Expedient of introduction fractional integro – differentiations in a quantum statistical physics. Some properties of systems with fractional – a sedate spectrum


Z. Z. Alisultanov, R. P. Mejlanov

Using a source function method attempt of introduction of fractional derivatives on co-ordinate and on time in system of many particles is made. The basic idea consists that interaction between particles can lead to change of dependence of a kinetic energy from an impulse. Being grounded on this fact it is possible to guess, that interaction can lead to fractionally power characteristic, so and to fractional derivatives on co-ordinate. Further, connection between function of interaction of quasi-particles and fractionally power characteristic is established. Such approach allows to understand most accurately physics of the process featured by the equations of the fractional order. Expression for a density of states for gas with fractionally sedate spectrum is gained. The deduction about occurrence possibility fractional structures in such system becomes. The equation of state of gas with fractional – a sedate spectrum is gained.

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