Diffusion and Current of Brownian Particles in Tilted Piecewise Linear Potentials: Amplification and Coherence

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the non-monotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Peclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.Comment: To appear in PR

Three and four current reversals versus temperature in correlation ratchets with a simple sawtooh potential

Transport of Brownian particles on a simple sawtooth potential subjected to both unbiased thermal and nonequilibrium symmetric three-level Markovian noise is considered. The new effects of three and four current reversals as a function of temperature are established in such correlation ratchets. The parameter space coordinates of the fixed points associated with these current reversals and the necessary and sufficient conditions for the existence of the novel current reversals are found.Comment: 4 pages, 5 figures; some changes introduced; accepted for publication in Physical Review

A new approach to electromagnetic wave tails on a curved spacetime

We present an alternative method for constructing the exact and approximate solutions of electromagnetic wave equations whose source terms are arbitrary order multipoles on a curved spacetime. The developed method is based on the higher-order Green's functions for wave equations which are defined as distributions that satisfy wave equations with the corresponding order covariant derivatives of the Dirac delta function as the source terms. The constructed solution is applied to the study of various geometric effects on the generation and propagation of electromagnetic wave tails to first order in the Riemann tensor. Generally the received radiation tail occurs after a time delay which represents geometrical backscattering by the central gravitational source. It is shown that the truly nonlocal wave-propagation correction (the tail term) takes a universal form which is independent of multipole order. In a particular case, if the radiation pulse is generated by the source during a finite time interval, the tail term after the primary pulse is entirely determined by the energy-momentum vector of the gravitational field source: the form of the tail term is independent of the multipole structure of the gravitational source. We apply the results to a compact binary system and conclude that under certain conditions the tail energy can be a noticeable fraction of the primary pulse energy. We argue that the wave tails should be carefully considered in energy calculations of such systems.Comment: RevTex, 28 pages, 5 eps figures, http://www.tpu.ee/~tony/texdocs/, 4 changes made (pp. 2, 4, 22, 24), 2 references adde

An alternative way to derive the geodesic deviation equation for rapidly diverging geodesics

We present a derivation of the equation of geodesic deviation under the assumption that the geodesics are adjacent in some neighbourhood, but their rate of separation is arbitrary. The resulting modified equation of geodesic deviation is nonlinear, it reduces to the ordinary linear geodesic deviation equation when the changes of position of corresponding points on the two geodesics as well as the changes of directions of the corresponding tangents are small. Our derivation is straightforward but shorter and more lucid than the earlier ones. Some of the consequences of the modified equation are also discussed