Ratchet motion and current reversal of Brownian motors coupled by birth-death interactions in the crowded environment

Ratchet universality in the bidirectional escape from a symmetric potential well

“…For deterministic ratchets, the effectiveness of the theory of ratchet universality has been demonstrated in diverse physical contexts in which the driving forces are chosen to be biharmonic, such as in the cases of cold atoms in optical lattices [27,28], topological solitons [29], Bose-Einstein condensates exposed to a sawtoothlike optical lattice potential [30], matter-wave solitons [31], and one-dimensional granular chains [32]. Also, the interplay between thermal noise and symmetry breaking in the directed ratchet transport (DRT) of a Brownian particle moving on a periodic substrate subjected to a homogeneous temporal biharmonic force [33][34][35] as well as the cases of a driven Brownian particle subjected to a vibrating periodic potential [26], a driven Brownian particle in the presence of non-Gaussian noise [36], and coupled Brownian motors with stochastic interactions in the crowded environment [37] have been explained quantitatively in coherence with the degree-of-symmetry-breaking (DSB) mechanism, as predicted by the theory of ratchet universality [24,25].…”

“…where cn (•; m) and sn (•; m) are Jacobian elliptic functions [37] of parameter m, and ≡ 2K (m)/T , with K (m) being the complete elliptic integral of the first kind [38].…”

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

“…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. Additionally, RU has recently been demonstrated in the bidirectional escape from a symmetric potential well [23].…”

Ratchet universality in coupled dissipative oscillators without external bias

“…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].…”