Chemistry, Physics and Technology of Surface

ISSN 2518-1238 (Online), ISSN 2079-1704 (Print)

It is known that widths of spectral lines provide а researcher with a variety of important information: about properties of materials, nature of particles interaction, physical parameters of an environment, etc. By analogy with a study of spectral lines, this article analyzes behavior of the width of a bell-shaped frequency dependence of the average velocity of Brownian particles described by a model of a stochastic Brownian motor with asymmetric dichotomous fluctuations of particle potential energy. The bell-shaped dependence is explained by the disappearance of the motor effect in both the low- and high-frequency limits. The relations for the average particle velocity in the adiabatic (low-frequency) and high-temperature regimes of motion allowed us to analyze the frequency dependences for different values of the temporal asymmetry parameter ε of the fluctuations and the ratio α of potential energy amplitudes in two states of the dichotomous process. The invariance of characteristics of an adiabatic Brownian motor with respect to the asymmetry parameter allowed us to assume the effect of one-sided broadening of the frequency dependence of the velocity with changing ε and α.

To confirm this assumption, the high-temperature behavior of a Brownian motor with a biharmonic potential energy (described by a sum of two sinusoids) is considered. Graphic dependences of the average velocity on the fluctuation frequency are obtained, which coincide in the adiabatic regime of motor functioning. Using the numerical procedure, frequencies of maxima and widths of the distributions have been calculated dependent on the temporal asymmetry parameter of fluctuations ε and the ratio α. The calculated dependences confirmed the assumption about the one-sided broadening of the bell-shaped frequency dependence of the average velocity of a Brownian motor.

stochastic fluctuation processes; diffusion transport; Brownian motors; broadening of bell-shaped distributions

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