Pinning and depinning of a classic quasi-one-dimensional Wigner crystal in the presence of a constriction

We studied the dynamics of a quasi-one-dimensional chain-like system of charged particles at low temperature, interacting through a screened Coulomb potential in the presence of a local constriction. The response of the system when an external electric field is applied was investigated. We performed Langevin molecular dynamics simulations for different values of the driving force and for different temperatures. We found that the friction together with the constriction pins the particles up to a critical value of the driving force. The system can depin \emph{elastically} or \emph{quasi-elastically} depending on the strength of the constriction. The elastic (quasi-elastic) depinning is characterized by a critical exponent $\beta\sim0.66$ ($\beta\sim0.95$). The dc conductivity is zero in the pinned regime, it has non-ohmic characteristics after the activation of the motion and then it is constant. Furthermore, the dependence of the conductivity with temperature and strength of the constriction was investigated in detail. We found interesting differences between the single and the multi-chain regimes as the temperature is increased.Comment: 18 pages, 16 figures, accepted for publication in PR

Generalized Drude model: Unification of ballistic and diffusive electron transport

For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean free path and arbitrary shape of the conduction band edge profile. Universal formulas are obtained for the current-voltage characteristic in the nondegenerate case and for the zero-bias conductance in the degenerate case, which describe in a transparent manner the interplay of ballistic and diffusive transport. The semiclassical approach is adopted, but quantum corrections allowing for tunneling are included. Examples are considered, in particular the case of chains of grains in polycrystalline or microcrystalline semiconductors with grain size comparable to, or smaller than, the mean free path. Substantial deviations of the results of the unified model from those of the ballistic thermionic-emission model and of the drift-diffusion model are found. The formulation of the model is one-dimensional, but it is argued that its results should not differ substantially from those of a fully three-dimensional treatment.Comment: 14 pages, 5 figures, REVTEX file, to appear in J. Phys.: Condens. Matte

Anomalous Drude Model

A generalization of the Drude model is studied. On the one hand, the free motion of the particles is allowed to be sub- or superdiffusive; on the other hand, the distribution of the time delay between collisions is allowed to have a long tail and even a non-vanishing first moment. The collision averaged motion is either regular diffusive or L\'evy-flight like. The anomalous diffusion coefficients show complex scaling laws. The conductivity can be calculated in the diffusive regime. The model is of interest for the phenomenological study of electronic transport in quasicrystals.Comment: 4 pages, latex, 2 figures, to be published in Physical Review Letter

Directional statistics and filtering using libDirectional

In this paper, we present libDirectional, a MATLAB library for directional statistics and directional estimation. It supports a variety of commonly used distributions on the unit circle, such as the von Mises, wrapped normal, and wrapped Cauchy distributions. Furthermore, various distributions on higher-dimensional manifolds such as the unit hypersphere and the hypertorus are available. Based on these distributions, several recursive filtering algorithms in libDirectional allow estimation on these manifolds. The functionality is implemented in a clear, well-documented, and object-oriented structure that is both easy to use and easy to extend

Optical activity induced by curvature in a gravitational pp-wave background

We study optical activity induced by curvature. The optical activity model we present has two phenomenological gyration parameters, within which we analyze three model cases, namely, an exactly integrable model, the Landau-Lifshitz model and the Fedorov model, these latter two are solved in the short wavelength approximation. The model background is a gravitational pp-wave. The solutions show that the optical activity induced by curvature leads to Faraday rotation.Comment: 16 pages, late