Controlling directed ratchet transport of driven overdamped Brownian particles subjected to a vibrating periodic potential: ratchet universality versus harmonic-mixing perturbation theory

Abstract

We study directed ratchet transport of a harmonically driven overdamped Brownian particle subjected to a harmonically shaken periodic potential. The existence of a frequency-dependent optimal value of the relative amplitude of the two harmonic excitations involved is theoretically predicted from the criticality scenario giving rise to ratchet universality and numerically confirmed by extensive numerical experiments. The robustness of the ratchet universality scenario is also demonstrated when the external harmonic excitation is replaced by a bounded chaotic excitation having the same underlying main frequency in its Fourier spectrum. We remark that our findings are in sharp contrast with the predictions from the standard harmonic-mixing perturbation theory.

Directed ratchet transport of cold atoms and fluxons driven by biharmonic fields: A unified view

“…[16]). There have also been quantitative explanations in coherence with the degree-of-symmetry-breaking mechanism, as predicted by the theory of RU [11,12], of the interplay between thermal noise and symmetry breaking in the DRT of a Brownian particle moving on a periodic substrate subjected to a homogeneous temporal biharmonic force [17][18][19], and of a driven Brownian particle subjected to a vibrating periodic potential [20]. Numerical analyses of a driven Brownian particle in the presence of non-Gaussian noise [21] and coupled Brownian motors with stochastic interactions in a crowded environment [22] have confirmed the RU predictions.…”

Ratchet universality in coupled dissipative oscillators without external bias

“…The effectiveness of RU theory has been demonstrated in diverse physical contexts. Instances are cold atoms in optical lattices [22,23], topological solitons [10], Bose-Einstein condensates exposed to a sawtoothlike optical lattice potential [24], matterwave solitons [25], one-dimensional granular chains [26], Brownian particles moving on a periodic substrate subjected to a homogeneous temporal biharmonic excitation [27][28][29], Bose-Einstein condensates under an unbiased periodic driving potential [30], and driven overdamped Brownian particles subjected to a vibrating periodic potential [31]. Also, numerical analyses of a driven Brownian particle in the presence of non-Gaussian noise [32] and coupled Brownian motors with stochastic interactions in a crowded environment [33] have confirmed the RU predictions, and RU has recently been demonstrated in the bidirectional escape from a symmetric potential well [34].…”