B.I. Yakubovich1

1 Petersburg Nuclear Physics Institute named by B.P. Konstantinov (Gatchina, Russia)

Fluctuation phenomena are widely studied in various physical systems. Fluctuation studies are important both for studying the nature of physical phenomena and for solving applied problems. Fluctuation phenomena have a very diverse physical origin. Fluctuations in a very large number of cases are random impulse processes. In this regard, it is expedient to consider fluctuations related to random impulse processes in a fairly general form and give their quantitative description. This could give a more complete and rigorous description of fluctuations, applicable to fluctuation phenomena of various physical nature, and contribute to the solution of a number of applied problems. The purpose of the work: to consider in fairly general form fluctuations in physical systems, which are random impulse processes; calculate spectra of fluctuations, both in general cases and in specific most significant cases.

Fluctuations in physical systems are considered. This is done in the following way. Fluctuations, which are random impulse processes, are considered. Next impulse is caused by an event of a random process of one or another physical origin, leading to fluctuations. Fluctuations are analyzed in a very general case. Fluctuations are considered as the following random sequence of pulses of a very general form. Pulses are statistically related: the amplitude of a pulse is statistically related to the amplitude and duration of the preceding pulse. Pulse parameters (duration and amplitude) are statistically related. Statistical relationships and distributions of parameters are given in general form. The pulses have an arbitrary shape. This fluctuations is analyzed and the fluctuation spectrum is calculated. As a result, a rigorous quantitative description of such fluctuations in physical systems is given, and a general expression for spectrum of fluctuations is calculated. Next, the following is done. A step-by-step simplification of general expression for the spectrum is carried out. An expression is determined for the fluctuation spectrum for statistically independent pulses. An expression is found for the spectrum of fluctuations in the case when pulse parameters are statistically independent. Note that obtained formulas are quite general, since statistical relationships and distributions of pulse parameters are given in a general form. Next, fluctuations in physical systems are analyzed in specific most significant cases. Fluctuation processes with probability distributions widely encountered in physics are considered. Expressions for the spectra are calculated in such cases.

As a result, a rigorous and broad description of fluctuations in physical systems is given, which is applicable to numerous fluctuation phenomena of various physical nature. It allows one to directly determine spectral characteristics and properties of fluctuations in different objects for processes that have different physical origins. For applied purposes, this makes it possible to reduce noise of electronic devices and increase their reliability.

Yakubovich B.I. Fluctuations in physical systems. Electromagnetic waves and electronic systems. 2023. V. 28. № 4. P. 28−35. DOI: https://doi.org/10.18127/j15604128-202304-03 (in Russian)

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