Use and misuse of adiabatic elimination procedures for stochastic processes

The extension of the current adiabatic elimination procedures to stochastic processes in the presence of external noises is criticized. Limitations pointed out in the recent literature are traced back to preparation phase effects that are shown to be unavoidable in the absence of analytical expressions for the stationary distributions.     

Noise-assisted transport on symmetric periodic substrates

The rectification of a massive Brownian particle moving on a periodic substrate can be achieved in the absence of spatial asymmetry, by having recourse to (at least) two periodic, zero-mean input signals. We determine the relevant drift current under diverse operation conditions, namely, additive and multiplicative couplings, adiabatic and fast oscillating drives, and propagating substrate modulations. Distinct rectification mechanisms result from the interplay of noise and commensuration of the input frequencies, mediated through the nonlinearity of the substrate. These mechanisms are then extended to characterize soliton transport along a directed multistable chain. As the side-wise soliton diffusion is ultimately responsible for the transverse diffusion of such chains, our approach provides a full account of the Brownian motion of both pointlike and linear objects on a periodic substrate.     

Controlling the motion of magnetic flux quanta

We study the transport of vortices in superconductors with triangular arrays of boomerang- or V-shaped asymmetric pinning wells, when applying an alternating electrical current. The asymmetry of the pinning landscape induces a very efficient "diode" effect, that allows the sculpting at will of the magnetic field profile inside the sample. We present the first quantitative study of magnetic "lensing" of fluxons inside superconductors. Our proposed vortex lens provides a near threefold increase of the vortex density at its "focus" regions. The main numerical features have been derived analytically.     

Controlling transport in mixtures of interacting particles using Brownian motors

An outstanding open problem in nanoscience is how to control the motion of tiny particles. Ratchetlike devices, inspired by biological motors, have been proposed as a way to achieve this goal. However, the net directed transport is almost suppressed if the diffusing particles are weakly coupled to the underlying spatially asymmetric substrate. Here we show how adding particles of an auxiliary species, that interact with both the primary particles of interest and the substrate, provides a controlled enhancement of the flow for both species. These can move either together or in opposite directions, depending upon the strength of the interaction, and whether it is attractive or repulsive.     

The moment problem in statistical mechanics: Correlation functions of purely dissipative systems

The question of convergence of the Mori formalism is investigated in the frame of the classical theory of moments. The autocorrelation functions (acfs) of purely dissipative systems admit of both moment and continued fraction expansions (like that obtained by Mori). New physical conditions for the convergence of the latter ones are related to the analytical behaviour of the corresponding spectral moment sequences. From discussion of the analytical properties of such continued fractions it is also proved that the knowledge of the spectral moments does not suffices for determining infinite acf eigenvalue spectra. Mori's continued fraction always converges at zero frequency, thus reproducing the value of the acf relaxation time correctly. Finally, our predictions are verified by comparison with the analytical results for the Verhulst model published recently by Jung and Risken.     

Nonlinear budó model for dielectric relaxation: Comparison with new experimental data

Zeitschrift für Physik B Condensed Matter -