Joseph P. Straley

Phase diagram of one-dimensional driven lattice gases with open boundaries

We consider the asymmetric simple exclusion process (ASEP) with open boundaries and other driven stochastic lattice gases of particles entering, hopping and leaving a one- dimensional lattice. The long-term system dynamics, stationary states, and the nature of phase transitions between steady states can be understood in terms of the interplay of two characteristic velocities, the collective velocity and the shock (domain wall) velocity. This interplay results in two distinct types of domain walls whose dynamics is computed. We conclude that the phase diagram of the ASEP is generic for one-component driven lattice gases with a single maximum in the current-density relation.

Distribution-induced non-universality of the percolation conductivity exponents

The power law which characterises the behaviour of the conductivity of an inhomogeneous conductor near the percolation threshold should generally be independent of the distribution from which the conducting elements are chosen. Some counterexamples, in which a sufficiently anomalous distribution can alter the conduction threshold exponents, are exhibited. Specifically, it is claimed that a network randomly composed of insulating bonds ( sigma =0) and bonds chosen from a distribution behaving as sigma - alpha for small sigma will give the usual exponent t for alpha 2, but in the case 1< beta <or=2 the excess of large conductances alters the exponent to S=s+(2- beta )/( beta -1).

Low-Dimensional Bose Liquids: Beyond the Gross-Pitaevskii Approximation

The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions

Critical phenomena in resistor networks

d\ensuremath{\le}2

The ant in the labyrinth: diffusion in random networks near the percolation threshold

, and we propose the appropriate low-dimensional modifications, which have a universal form. For

The bicritical macroscopic conductivity exponent in dimensionalities two, three and infinity

d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

Random resistor tree in an applied field

we analyze density profiles in confining potentials, superfluid properties, solitons, and self-similar solutions.

Deconfinement and dissipation in quantum Hall Josephson tunneling.

The conduction threshold which occurs in resistor networks when a certain fraction has zero conductivity can be treated as a sort of critical point. This critical point is also relevant to mixtures of resistors with finite conductivities a and b, in the limit a<<b. A homogeneous function representation is proposed for the conductivity in the vicinity of the conduction threshold and a parametric representation is also given. This representation makes predictions for the concentration (p) and composition (a/b) dependence of such networks which are consistent with the behaviour of the Bethe lattice model recently proposed by Stinchcombe (1973, 1974). The frequency dependence of the impedance is also discussed and a correlation length which diverges at the critical point is described.

Conductivity anisotropy and the Hall effect in inhomogeneous conductors near the percolation threshold

The parameters which describe the mean-squared displacement (R2(t)) of a random walker on a random network have a characteristic singular dependence on epsilon =(p-pc)/pc near the percolation threshold. The critical exponents, which characterise the singularities of the diffusion constant, moment of inertia of finite clusters, and time constants for development of the long-time behaviour, are related by a scaling theory. They may also be related to the exponent theories for the percolation and percolation conduction problems. An equivalent resistor network can be described which is equivalent to the time Laplace transform of the diffusion problem. These problems will be given explicit treatment for the Cayley tree.

Dimensionality-dependent scaling relations for conduction exponents

The authors present values of the bicritical macroscopic conductivity exponent nu , which was recently defined for the random resistor lattice. For dimensionality D=2, the value is obtained exactly by exploiting the properties of the dual lattice. In three dimensions a potential problem is solved approximately on a 34*34*34 computer-simulated cubic lattice. For infinite dimensionality, the exponent is extracted by treating the Cayley tree lattice. The authors find: nu (D=2)=0(exact); nu (D=3)=0.78+or-0.10; nu (D= infinity )=2(exact). Knowledge of the nu exponent is shown to be a necessary prerequisite for a complete understanding of the critical behaviour of multiphase inhomogeneous conducting systems.