Condensed Matter Theory

Abstract:

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the spectral gap, which characterizes the approach to stationarity at large times. We observe boundary induced crossovers in and between massive, diffusive, and Kardar-Parisi-Zhang scaling regimes.

Abstract:

The use of multi-antenna arrays in wireless communications through disordered media promises huge increases in the information transmission rate. It is therefore important to analyse the information capacity of such systems in realistic situations of microwave transmission, where the statistics of the transmission amplitudes (channel) may be coloured. Here, we present an approach that provides analytic expressions for the statistics, i.e. the moments of the distribution, of the mutual information for general Gaussian channel statistics. The mathematical method applies tools developed originally in the context of coherent wave propagation in disordered media, such as random matrix theory and replicas. Although it is valid formally for large antenna numbers, this approach produces extremely accurate results even for arrays with as few as two antennas. We also develop a method to analytically optimize over the input signal distribution, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel. The emphasis of this paper is on elucidating the novel mathematical methods used. We do this by analysing a specific case when the channel matrix is a complex Gaussian with arbitrary mean and unit covariance, which is usually called the Ricean channel. © 2005 IOP Publishing Ltd.

Abstract:

A formulation is developed for the calculation of the electromagnetic-fluctuation forces for dielectric objects of arbitrary geometry at small separations, as a perturbative expansion in the dielectric contrast. The resulting Lifshitz energy automatically takes on the form of a series expansion of the different many-body contributions. The formulation has the advantage that the divergent contributions can be readily determined and subtracted off, and thus makes a convenient scheme for realistic numerical calculations, which could be useful in designing nanoscale mechanical devices.

Abstract:

We explore the conditions under which colloids can be stabilized by the addition of smaller particles. The largest repulsive barriers between colloids occur when the added particles repel each other with soft interactions, leading to an average accumulation near the colloid surfaces. At lower densities these diffuse layers of mobile particles (nanoparticle halos) result in stabilization, but when too many are added, the interactions become attractive again. We systematically study these effects -accumulation repulsion, re-entrant attraction, and bridging - by accurate and flexible integral equation techniques[1], which faithfully reproduce recent computer simulations of the same effect[2]. We can explain recent experiments[3], and moreover show that there is a very substantial parameter regime where nanoparticle halos lead to colloidal stabilisation. We argue that this new mechanism should be widely applicable and complimentary to exisiting steric and charge stabilization techniques. It may should also be relevant for smaller scale biological interactions.