Canonical Representations Related to Hyperbolic Spaces

AbstractWe extend the notion of canonical representation, introduced by A. M. Vershik, I. M. Gel'fand and M. I. Graev (1982, in “Representation Theory,” Cambridge Univ. Press, Cambridge, U.K.), to all (classical) rank one semisimple Lie groups. We determine the spectral decomposition of the canonical representations in detail

Focusing in Multiwell Potentials: Applications to Ion Channels

We investigate out of equilibrium stationary distributions induced by a stochastic dichotomous noise on double and multi-well models for ion channels. Ion-channel dynamics is analyzed both through over-damped Langevin equations and master equations. As a consequence of the external stochastic noise, we prove a non trivial focusing effect, namely the probability distribution is concentrated only on one state of the multi-well model. We also show that this focusing effect, which occurs at physiological conditions, cannot be predicted by a simple master equation approach.Comment: 8 pages, 7 figure

On a certain class of semigroups of operators

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.Comment: 11 page

Time-Dependent Density Functional Theory for Driven Lattice Gas Systems with Interactions

We present a new method to describe the kinetics of driven lattice gases with particle-particle interactions beyond hard-core exclusions. The method is based on the time-dependent density functional theory for lattice systems and allows one to set up closed evolution equations for mean site occupation numbers in a systematic manner. Application of the method to a totally asymmetric site exclusion process with nearest-neighbor interactions yields predictions for the current-density relation in the bulk, the phase diagram of non-equilibrium steady states and the time evolution of density profiles that are in good agreement with results from kinetic Monte Carlo simulations.Comment: 11 pages, 3 figure

Biased Brownian motion in extreme corrugated tubes

Biased Brownian motion of point-size particles in a three-dimensional tube with smoothly varying cross-section is investigated. In the fashion of our recent work [Martens et al., PRE 83,051135] we employ an asymptotic analysis to the stationary probability density in a geometric parameter of the tube geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. Expression for the higher order corrections to the probability density are derived. Using this expansion orders we obtain that in the diffusion dominated regime the average particle current equals the zeroth-order Fick-Jacobs result corrected by a factor including the corrugation of the tube geometry. In particular we demonstrate that this estimate is more accurate for extreme corrugated geometries compared to the common applied method using the spatially dependent diffusion coefficient D(x,f). The analytic findings are corroborated with the finite element calculation of a sinusoidal-shaped tube.Comment: 10 pages, 4 figure

Entropic Stochastic Resonance

We present a novel scheme for the appearance of Stochastic Resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. This Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single-molecules and nano-devices.Comment: 4 pages, 3 figure