Vibrational ratchets

Transport in a one-dimensional symmetric device can be activated by the combination of thermal noise and a bi-harmonic drive. For the study case of an overdamped Brownian particle diffusing on a periodic one-dimensional substrate, we distinguish two apparently different bi-harmonic regimes: (i) Harmonic mixing, where the two drive frequencies are commensurate and of the order of some intrinsic dynamical relaxation rate. A comparison of new simulation results with earlier theoretical predictions shows that the analytical understanding of this frequency mixing mechanism is not satisfactory, yet; (ii) Vibrational mixing, where one harmonic drive component is characterized by a high frequency but finite amplitude-to-frequency ratio. Its effect on the device response to either a static or a low-frequency additional input signal is accurately reproduced by rescaling each spatial Fourier component of the substrate potential, separately. Contrary to common wisdom based on the linear response theory, we show that extremely high-frequency modulations can indeed influence the response of slowly (or dc) operated devices, with potential applications in sensor technology and cellular physiology. Finally, the mixing of two high-frequency beating signal is also investigated both numerically and analytically.Comment: 8 pages, 9 figure

Recycled Noise Rectification: A Dumb Maxwell's Daemon

The one dimensional motion of a massless Brownian particle on a symmetric periodic substrate can be rectified by re-injecting its driving noise through a realistic recycling procedure. If the recycled noise is multiplicatively coupled to the substrate, the ensuing feed-back system works like a passive Maxwell's daemon, capable of inducing a net current that depends on both the delay and the autocorrelation times of the noise signals. Extensive numerical simulations show that the underlying rectification mechanism is a resonant nonlinear effect: The observed currents can be optimized for an appropriate choice of the recycling parameters with immediate application to the design of nanodevices for particle transport.Comment: 7 pages, 6 figure

Detectable inertial effects on Brownian transport through narrow pores

We investigate the transport of suspended Brownian particles dc driven along corrugated narrow channels in a regime of finite damping. We demonstrate 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 both, the temperature and the strength of the dc drive. Therefore, transport through sufficiently narrow constrictions turns out to be sensitive to the viscosity of the suspension fluid. Applications to colloidal systems are discussed

AC Driven Jumps Distribution on a Periodic Substrate

A driven Brownian particle (e.g. an adatom on a surface) diffusing on a low-viscosity, periodic substrate may execute multiple jumps. In the presence of an additional periodic drive, the jump lengths and time durations become statistically modulated according to a syncronyzation mechanism reminiscent of asymmetric stochastic resonance. Here, too, bistability plays a key role, but in a dynamical sense, inasmuch as a particle switches between locked and running states.Comment: 4 pages, 4 figures, RevTeX, to be published in Surface Science Letter

Deterministic ratchets: route to diffusive transport

The rectification efficiency of an underdamped ratchet operated in the adiabatic regime increases according to a scaling current-amplitude curve as the damping constant approaches a critical threshold; below threshold the rectified signal becomes extremely irregular and eventually its time average drops to zero. Periodic (locked) and diffusive (fully chaotic) trajectories coexist on fine tuning the amplitude of the input signal. The transition from regular to chaotic transport in noiseless ratchets is studied numerically.Comment: 9 pages, 5 figures, to be published in Phys. Rev.

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

Noise sustained propagation: Local versus global noise

We expand on prior results on noise supported signal propagation in arrays of coupled bistable elements. We present and compare experimental and numerical results for kink propagation under the influence of local and global fluctuations. As demonstrated previously for local noise, an optimum range of global noise power exists for which the medium acts as a reliable transmission ``channel''. We discuss implications for propagation failure in a model of cardiac tissue and present a general theoretical framework based on discrete kink statistics. Valid for generic bistable chains, the theory captures the essential features ob served in our experiments and numerical simulations.Comment: 1 latex file 20 pages, 9 figures. Accepted for publication in Physical Review

Bistable Flow Driven by Coloured Gaussian Noise: A Critical Case Study

A one dimensional flow driven by additive Gaussian noise is considered. Possible pitfalls in the use of Langevin equations of non-Markovian processes are identified. In particular, the stationarity of the random force in a non-Markovian Langevin equation does not imply that the dynamics of the non-Markovian process is consistent with an initial stationary preparation scheme. The small relaxation time Fokker-Planck approximation schemes put forward in the recent literature are applied and it is pointed out that those schemes may lead to unreliable predictions. The results for the activation rate as evaluated from the approximative Fokker-Planck schemes does not coincide in leading order in τ (Arrhenius factor) with a computer simulation for small noise intensity: thus showing that the wings of the stationary probability p̄(x) are in leading order in τ not recovered from the approximative Fokker-Planck schemes

Numerical Solution for Diffusion in Periodic Potentials: A Comparison with the Theory of Activated Processes

A numerical algorithm is implemented so as to explore brownian particle diffusion in a periodic potential throughout the full viscosity range. The predictions of the theory of activated processes are checked. In particular, a recent refinement of the vanishingly small viscosity limit of the Kramers approach by Büttiker et al. (Phys. Rev. B28 1268 (1983)) is found to fit better our numerical results