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The phenomenon of drift motion of single-domain ferromagnetic particles induced by the Magnus force in a viscous fluid is studied analytically. We use a minimal set of equations to describe the translational and rotational motions of these particles subjected to a harmonic force and a non-uniformly rotating magnetic field. Assuming that the azimuthal angle of the magnetic field is a periodic triangular function, we analytically solve the rotational equation of motion in the steady state and calculate the drift velocity of particles. We study in detail the dependence of this velocity on the model parameters, discuss the applicability of the drift phenomenon for separation of particles in suspensions, and verify numerically the analytical predictions., Comment: 20 pages, 7 figures

We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second moments of the particle position as inverse Laplace transforms. By applying to these transforms the ordinary and the modified Tauberian theorem, we determine the short- and long-time behavior of the mean-square displacement of particles. Our results show that while at short times the biased diffusion is always ballistic, at long times it can be either normal or anomalous. We formulate the conditions for normal and anomalous behavior and derive the laws of biased diffusion in both these cases., Comment: 11 pages, 3 figures

We study directed transport of overdamped particles in a periodically rocked random sawtooth potential. Two transport regimes can be identified which are characterized by a nonzero value of the average velocity of particles and a zero value, respectively. The properties of directed transport in these regimes are investigated both analytically and numerically in terms of a random sawtooth potential and a periodically varying driving force. Precise conditions for the occurrence of transition between these two transport regimes are derived and analyzed in detail., Comment: 18 pages, 7 figures

We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the probability density of the arrival time. We explicitly calculate the path integral for a special case of dichotomous disorder and use the corresponding characteristic function to derive prominent properties of the arrival time probability density. Specifically, we establish the scaling properties of the central moments, analyze the behavior of the probability density for short, long, and intermediate distances. In order to quantify the deviation of the arrival time distribution from a Gaussian shape, we evaluate the skewness and the kurtosis., Comment: 18 pages, 5 figures

We perform a time-dependent study of the driven dynamics of overdamped particles which are placed in a one-dimensional, piecewise linear random potential. This set-up of spatially quenched disorder then exerts a dichotomous varying random force on the particles. We derive the path integral representation of the resulting probability density function for the position of the particles and transform this quantity of interest into the form of a Fourier integral. In doing so, the evolution of the probability density can be investigated analytically for finite times. It is demonstrated that the probability density contains both a $\delta$-singular contribution and a regular part. While the former part plays a dominant role at short times, the latter rules the behavior at large evolution times. The slow approach of the probability density to a limiting Gaussian form as time tends to infinity is elucidated in detail., Comment: 18 pages, 5 figures

We study analytically and numerically the overdamped, deterministic dynamics of a chain of {\it charged}, interacting particles driven by a longitudinal alternating electric field and additionally interacting with a smooth ratchet potential. We derive the equations of motion, analyze the general properties of their solutions and find the drift criterion for chain motion. For ratchet potentials of the form of a double-sine and a phase-modulated sine it is demonstrated that both, a so-called integer and fractional transport of the chain can occur. Explicit results for the directed chain transport for these two classes of ratchet potentials are presented., Comment: 17 pages, 8 figures

We study the equilibrium, oscillatory and transport properties of a chain of charged particles which interact with each other via the Coulomb and power-like repulsive interactions. Exact, analytical expressions for the energy of the ground state, interparticle distances, and vibration spectrum are derived, and the stability criterion for a chain with equidistant particles is established. We also consider the phenomenon of deterministic transport of a chain in a ratchet potential subject to a longitudinal alternating electric field., Comment: 25 pages, 6 figures, submitted to Phys. Rev. B

A statistical theory of the strip domain structure excited in a bubble film by an oscillating magnetic field is developed. The theory is based on the consideration of the strip domain structure as a thermodynamic system characterized by the spectrum of domain walls oscillation and an effective temperature that is caused by an oscillating magnetic field and film nonuniformities. We found the thermodynamic characteristics of that domain structure and calculated its period as a function of the frequency and amplitude of an oscillating magnetic field., Comment: 6 pages, 3 figures