Exactly solvable model of a slightly fluctuating ratchet.

We consider the motion of a Brownian particle in a sawtooth potential dichotomously modulated by a spatially harmonic perturbation. An explicit expression for the Laplace transform of the Green function of an extremely asymmetric sawtooth potential is obtained. With this result, within the approximation of small potential-energy fluctuations, the integration of the relations for the average particle velocity is performed in elementary terms.

Brownian motor with competing spatial and temporal asymmetry of potential energy.

A Brownian motor is considered which operates due to asymmetric dichotomic fluctuations of the spatially periodic asymmetric potential energy. As shown, the motion direction and stopping points of this motor are dictated by the competition between the spatial and temporal asymmetry of the potential energy (or solely by temporal asymmetry in the case that the potential energy sign fluctuates). For an asymmetric sawtooth potential, the Brownian-particle average velocity is calculated numerically as a function of certain parameters of the model, whereas the low-frequency and low-energy approximations allow the corresponding analytical relationships to be derived for an arbitrarily shaped potential profile.

Brownian dipole rotator in alternating electric field.

The study addresses the azimuthal jumping motion of an adsorbed polar molecule in a periodic n -well potential under the action of an external alternating electric field. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment as well as the frequency dependences of polarizability and the average angular velocity, the three quantities exhibiting conspicuous stochastic resonance. As shown, unidirectional rotation can arise only provided simultaneous modulation of the minima and maxima of the potential by an external alternating field.

Conventional and generalized efficiencies of flashing and rocking ratchets: analytical comparison of high-efficiency limits.

We consider two basic types of Brownian motors which generate directed motion in a periodic asymmetric piecewise-linear potential as a result of random half-period shifts of the potential relief (flashing ratchets) or due to a temporally asymmetric unbiased force applied to the system (rocking ratchets). Analytical relationships have been derived which enable the comparison of the upper limits for the conventional and generalized energy conversion efficiencies in these motors. As found, the increasing amplitude of a sawtooth potential (or the decreasing temperature) makes the conventional efficiency tend to the unity limit faster for a rocking ratchet (in the absence of temporal asymmetry) than for a flashing ratchet.

Two approaches toward a high-efficiency flashing ratchet.

For a flashing ratchet with periodic potentials fluctuating via random shifts of one-half period, a high efficiency is shown to result from two mechanisms. The previously reported one [Yu. A.