Nonlinear Phenomena in Complex Systems, 2026, Vol.29, No.2, pp.105

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2026, Vol.29, No.2, pp.105 - 112

Brownian Ratchet with Dichotomous Fluctuations of the Biharmonic Potential Amplitude: Langevin Modeling and a High-temperature Expansion of the Average Velocity

F. A. Krasnov, I. V. Shapochkina, and V. M. Rozenbaum

We consider the motion of a Brownian particle in a periodic asymmetric biharmonic potential profile, the amplitude of which undergoes symmetric dichotomous fluctuations. The ratchet effect arising in this system is investigated using two approaches: Langevin modeling and an expansion of the average velocity in terms of the ratio of the biharmonic potential amplitudes to the thermal energy, accurate to fifth-order terms. Both approaches yielded consistent results. Including the fifth-order terms revealed the role of the first harmonic in forming the bell-shaped frequency dependence of the average ratchet velocity and demonstrated the dominance of the contribution of the average potential over the fluctuating component with increasing fluctuation frequency. For ratchet parameters near the applicability limit of the high-temperature expansion, the Langevin modeling reproduces the average ratchet velocity with a relative error of 1.4% and 0.3%, relative to the analytical results obtained using the third- and fifth-order perturbation theory, respectively.

Key words: nanoparticle, nonequilibrium fluctuations, Brownian motors

DOI: https://doi.org/10.5281/zenodo.21104323

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