Temperature-resonant cyclotron spectra in confined geometries

We consider a two-dimensional gas of colliding charged particles confined to finite size containers of various geometries and subjected to a uniform orthogonal magnetic field. The gas spectral densities are characterized by a broad peak at the cyclotron frequency. Unlike for infinitely extended gases, where the amplitude of the cyclotron peak grows linearly with temperature, here confinement causes such a peak to go through a maximum for an optimal temperature. In view of the fluctuation-dissipation theorem, the reported resonance effect has a direct counterpart in the electric susceptibility of the confined magnetized gas

Brownian motors: current fluctuations and rectification efficiency

With this work we investigate an often neglected aspect of Brownian motor transport: The r\^{o}le of fluctuations of the noise-induced current and its consequences for the efficiency of rectifying noise. In doing so, we consider a Brownian inertial motor that is driven by an unbiased monochromatic, time-periodic force and thermal noise. Typically, we find that the asymptotic, time- and noise-averaged transport velocities are small, possessing rather broad velocity fluctuations. This implies a corresponding poor performance for the rectification power. However, for tailored profiles of the ratchet potential and appropriate drive parameters, we can identify a drastic enhancement of the rectification efficiency. This regime is marked by persistent, uni-directional motion of the Brownian motor with few back-turns, only. The corresponding asymmetric velocity distribution is then rather narrow, with a support that predominantly favors only one sign for the velocity.Comment: 9 pages, 4 figure

Interaction of molecular motors can enhance their efficiency

Particles moving in oscillating potential with broken mirror symmetry are considered. We calculate their energetic efficiency, when acting as molecular motors carrying a load against external force. It is shown that interaction between particles enhances the efficiency in wide range of parameters. Possible consequences for artificial molecular motors are discussed.Comment: 6 pages, 8 figure

Driven Brownian transport through arrays of symmetric obstacles

We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely, when the constant drive is parallel to the principal or the diagonal array axes. This corresponds to studying the Brownian transport in periodic channels with reflecting walls of different topologies. The mobility and diffusivity of the transported particles in such channels are determined as functions of the drive and the array geometric parameters. Prominent transport features, like negative differential mobilities, excess diffusion peaks, and unconventional asymptotic behaviors, are explained in terms of two distinct lengths, the size of single obstacles (trapping length) and the lattice constant of the array (local correlation length). Local correlation effects are further analyzed by continuously rotating the drive between the two limiting orientations.Comment: 10 pages 13 figure

Brownian transport in corrugated channels with inertia

The transport of suspended Brownian particles dc-driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. Being such a diffusion length inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility and diffusivity, markedly differ for smoothly and sharply corrugated channels.Comment: 9 pages including figures. arXiv admin note: substantial text overlap with arXiv:1202.436

Phase space reduction of the one-dimensional Fokker-Planck (Kramers) equation

A pointlike particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the Fokker-Planck equation, which determines evolution of the particle density in phase space, onto the spatial coordinate x. The result is the Smoluchowski equation, valid in the overdamped limit, m->0, with a series of corrections expanded in powers of m. They are determined unambiguously within the recurrence mapping procedure. The method and the results are interpreted on the simplest model with no field and on the damped harmonic oscillator.Comment: 13 pages, 1 figur

Stokes' Drift of linear Defects

A linear defect, viz. an elastic string, diffusing on a planar substrate traversed by a travelling wave experiences a drag known as Stokes' drift. In the limit of an infinitely long string, such a mechanism is shown to be characterized by a sharp threshold that depends on the wave parameters, the string damping constant and the substrate temperature. Moreover, the onset of the Stokes' drift is signaled by an excess diffusion of the string center of mass, while the dispersion of the drifting string around its center of mass may grow anomalous.Comment: 14 pages, no figures, to be published in Phys.Rev.

Directed motion of domain walls in biaxial ferromagnets under the influence of periodic external magnetic fields

Directed motion of domain walls (DWs) in a classical biaxial ferromagnet placed under the influence of periodic unbiased external magnetic fields is investigated. Using the symmetry approach developed in this article the necessary conditions for the directed DW motion are found. This motion turns out to be possible if the magnetic field is applied along the most easy axis. The symmetry approach prohibits the directed DW motion if the magnetic field is applied along any of the hard axes. With the help of the soliton perturbation theory and numerical simulations, the average DW velocity as a function of different system parameters such as damping constant, amplitude, and frequency of the external field, is computed.Comment: Added references, corrected typos, extended introductio

Diffusion controlled initial recombination

This work addresses nucleation rates in systems with strong initial recombination. Initial (or `geminate') recombination is a process where a dissociated structure (anion, vortex, kink etc.) recombines with its twin brother (cation, anti-vortex, anti-kink) generated in the same nucleation event. Initial recombination is important if there is an asymptotically vanishing interaction force instead of a generic saddle-type activation barrier. At low temperatures, initial recombination strongly dominates homogeneous recombination. In a first part, we discuss the effect in one-, two-, and three-dimensional diffusion controlled systems with spherical symmetry. Since there is no well-defined saddle, we introduce a threshold which is to some extent arbitrary but which is restricted by physically reasonable conditions. We show that the dependence of the nucleation rate on the specific choice of this threshold is strongest for one-dimensional systems and decreases in higher dimensions. We discuss also the influence of a weak driving force and show that the transport current is directly determined by the imbalance of the activation rate in the direction of the field and the rate against this direction. In a second part, we apply the results to the overdamped sine-Gordon system at equilibrium. It turns out that diffusive initial recombination is the essential mechanism which governs the equilibrium kink nucleation rate. We emphasize analogies between the single particle problem with initial recombination and the multi-dimensional kink-antikink nucleation problem.Comment: LaTeX, 11 pages, 1 ps-figures Extended versio