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Article:

# Mathematical aspects of the study of fluctuation phenomena in solids

DOI 10.18127/j15604128-201904-02

Keywords:

B.I. Yakubovich – Ph.D.(Phys.-Math.), Senior Research Scientist, Petersburg Nuclear Physics Institute named by B.P. Konstantinov of NRC «Kurchatov Institute» (Gatchina)
E-mail: yakubovich_bi@pnpi.nrcki.ru

The fluctuation phenomena in solids are caused by numerous and diverse mechanisms. At the same time, mathematical description of fluctuations caused by various physical causes may have a lot in common. In this regard, it seems appropriate to consider from general positions fluctuations in solids, and to give their quantitative description, which could be used to analyze fluctuation phenomena having different physical nature. Consideration from general positions of fluctuations in solids is carried out in two directions: the sources of fluctuations are independent and the sources of fluctuations are statistically connections.
The fluctuation phenomena caused by independent sources of fluctuations are considered. The expression for the spectrum of fluctuations generated by an independent source is calculated. The obtained expression has enough general form: the distribution functions of the parameters of the fluctuation process are given in general form. Sources of fluctuations have very diverse nature, and, therefore, the calculated expression can be used to describe fluctuations having diverse physical origin.
Fluctuations in solids caused by statistically connected sources of fluctuations are considered. The spectrum of fluctuations caused by statistically connected sources in solids was calculated in an enough general form. As a result, a number of expressions of different degrees of generality were calculated for fluctuation spectra in solids caused by statistically connected sources of fluctuations. The obtained formulas can be applied to the analysis of fluctuation phenomena of different physical origin.
In article mathematical questions of the analysis of the fluctuation phenomena in solids are considered. Fluctuations in solids were analyzed from general positions, and expressions for fluctuation spectra were calculated. The fluctuation phenomena caused by a group of independent sources of fluctuations are considered. The fluctuation phenomena caused by statistically connected sources of fluctuations are considered. A series of expressions of various degrees of generality for the fluctuation spectra is calculated. The results obtained in the article can be widely applied to the study of fluctuation phenomena in solids and used to solve a number of applied problems.

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May 29, 2020

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