Adiabatic Discrete Ratchet Effect of a Rotor in the N-well Potential of Hindered Rotation

Abstract

We consider the azimuthal hopping motion of a polar rotor with a dipole moment µ in a periodic N-well potential of hindered rotation under the influence of adiabatic symmetric dichotomous fluctuations of an external electric field ±E with a period τ. A general expression is obtained for the average angular velocity Ω of unidirectional discrete rotation as a function of the direction ϕE of the applied field and the ratio ε = µE/kBT of the energy of the rotor-electric field interaction to thermal energy. The analysis of the symmetry of the obtained expression shows that the ratchet effect is absent for odd N, as well as for field orientations ϕE = 0, π/N, which coincide with the axes of potential wells and barriers with even N’s. With quadratic accuracy in ε ˝ 1, there is also no ratchet effect for N > 2. If N is even and ϕE = π/(2N), the absolute value of the average angular velocity is proportional to εN at ε ˝ 1 and tends to 2π/τ at ε/N2 ˛ 1. Graphical dependencies (τ/2π)Ω(ε, ϕE) are represented for N = 2, 4, 6, 8.