Force-dependent Fluxes of Adiabatic Classical and Quantum Rocking Ratchets

We consider the adiabatic mode of Brownian particle motion in a periodic potential under action symmetric dichotomous fluctuations an external force F with zero mean value (rocking ratchet), which fluctuation frequency is much less than inverse relaxation time each states process. Expressions are given for force-dependent fluxes classical rocking ratchet. In absence thermal fluctuations, within semiclassical approximation, analytical expressions obtained rocking-ratchet tunneling flux sawtooth arbitrary asymmetry and two sinusoids. It shown that has linear asymptotics modulus small due to (i) reverse respect direction (ii) root dependence integrand Gamow formula on energy. The main parameters model energy barrier V0 period L potentials, as well parameter ξ = l / width one its teeth equal l. quantum ratchet opposite corresponding limited range values |F| < αc , where changes from α1 (√5 − 1) 2 ≈ 0.618 extremely asymmetric (ξ α2 3 0.667 (ξ= 1 2). α2, sign change ξ. Numerical calculations sinusoids effective 0.655 lead similar results 0.81.