Rotational ratchet controlled by dichotomous changes in applied field orientations

Abstract

We explore the unidirectional rotation of a polar rotor (rotational ratchet) in a hindered-rotation potential (HRP), controlled by the dichotomous fluctuations of the orientation of the electric field. A symmetry analysis is carried out, which shows the absence of the ratchet effect for either an odd number of wells of the HRP or for an even number of wells if the average angle of the fluctuating orientations of the electric field coincides with any symmetry axes of the HRP. Analytical expressions are obtained for the average rotation velocity of the rotor in the double-well HRP in the low-temperature adiabatic approximation, when the hopping rotation occurs and thermodynamic equilibrium has time to be established in each state of the dichotomous process, and in the high-temperature approximation at arbitrary fluctuation frequencies, when the thermal energy is much greater than both the reorientation barrier of the HRP and the energy of the dipole rotor – electric field interaction. We showed that the maximum rotation velocity is achieved at large electric fields that fluctuate in sign, and the dependence of the rotation velocity on the amplitude of the angular fluctuations is bell-shaped, the width of which and the presence of the plateau can be tuned by the value of the average fluctuation angle. The dependence of the rotation velocity on the fluctuation frequency is also bell-shaped, wide for the stochastic fluctuations and narrow for the deterministic dichotomous ones, with the same linear low-frequency asymptotics.