arXiv subjects

R. K. P. Zia

Publications and source records attributed to R. K. P. Zia.

98 records · Page 6Linked to original sources

arXiv1998

Phase Transitions in a Driven Lattice Gas with Anisotropic Interactions

The Ising lattice gas, with its well known equilibrium properties, displays a number of surprising phenomena when driven into non-equilibrium steady states. We study such a model with anisotropic interparticle interactions ($J_{\Vert }\neq J_{\bot}$), using both Monte Carlo simulations and high temperature series techniques. Under saturation drive, the shift in the transition temperature can be both positive and negative, depending on the ratio $J_{\Vert }/J_{\bot}$! For finite drives, both first and second order transitions are observed. Some aspects of the phase diagram can be predicted by investigating the two point correlation function at the first non-trivial order of a high temperature series expansion.

cond-mat.stat-mech↗

arXiv1998

Driven Diffusive Systems: An Introduction and Recent Developments

Nonequilibrium steady states in driven diffusive systems exhibit many features which are surprising or counterintuitive, given our experience with equilibrium systems. We introduce the prototype model and review its unusual behavior in different temperature regimes, from both a simulational and analytic view point. We then present some recent work, focusing on the phase diagrams of driven bi-layer systems and two-species lattice gases. Several unresolved puzzles are posed.

cond-mat.stat-mech↗

arXiv1998

Two-point Correlations and Critical Line of the Driven Ising Lattice Gas in a High Temperature Expansion

Based on a high temperature expansion, we compute the two-point correlation function and the critical line of an Ising lattice gas driven into a non-equilibrium steady state by a uniform bias E. The lowest nontrivial order already reproduces the key features, i.e., the discontinuity singularity of the structure factor and the (qualitative) E-dependence of the critical line. Our approach is easily generalized to other non-equilibrium lattice models and provides a simple analytic tool for the study of the high temperature phase and its boundaries.

cond-mat.stat-mech↗

arXiv1997

Brownian-Vacancy Mediated Disordering Dynamics

The disordering of an initially phase segregated system of finite size, induced by the presence of highly mobile vacancies, is shown to exhibit dynamic scaling in its late stages. A set of characteristic exponents is introduced and computed analytically, in excellent agreement with Monte Carlo data. In particular, the characteristic time scale, controlling the crossover between increasing disorder and saturation, is found to depend on the exponent scaling the number of vacancies in the sample.

cond-mat.stat-mech↗

arXiv1997

Long Range Correlations in the Disordered Phase of a Simple Three State Lattice Gas

We investigate the dynamics of a three-state stochastic lattice gas, consisting of holes and two oppositely "charged" species of particles, under the influence of an "electric" field, at zero total charge. Interacting only through an excluded volume constraint, particles can hop to nearest neighbour empty sites. With increasing density and drive, the system orders into a charge-segregated state. Using a combination of Langevin equations and Monte Carlo simulations, we study the steady-state structure factors in the disordered phase where homogeneous configurations are stable against small harmonic perturbations. They show a discontinuity singularity at the origin which in real space leads to an intricate crossover between power laws of different kinds.

cond-mat.stat-mech↗

arXiv1997

Asymmetries in Structure Factor Histograms

We investigate the dynamics of a three-state stochastic lattice gas, consisting of holes and two oppositely "charged" species of particles, under the influence of an "electric" field, at zero total charge. Interacting only through an excluded volume constraint, particles can hop to nearest neighbour empty sites. Using a combination of Langevin equations and Monte Carlo simulations, we study the probability distributions of the steady-state structure factors in the disordered phase where homogeneous configurations are stable against small harmonic perturbations. Simulation and theoretical results are in excellent agreement, both showing asymmetric exponential distributions.

cond-mat.stat-mech↗

arXiv1997

Drifting Spatial Structures in a System with Oppositely Driven Species

A system consisting of two conservative, oppositely driven species of particles with excluded volume interaction alone is studied on a torus. The system undergoes a phase transition between a homogeneous and an inhomogeneous phase, as the particle densities are varied. Focusing on the inhomogeneous phase with generally unequal numbers of the two species, the spatial structure is found to drift counter-intuitively against the majority species at a constant velocity that depends on the external field, system size, and particle densities. Such dependences are derived from a coarse-grained continuum theory, and a microscopic mechanism for the drift is explained. With virtually no tuning parameter, various theoretical predictions, notably a field-system-size scaling, agree extremely well with the simulations.

cond-mat.stat-mech↗

arXiv1996

Periodic One-Dimensional Hopping Model with one Mobile Directional Impurity

Analytic solution is given in the steady state limit for the system of Master equations describing a random walk on one-dimensional periodic lattices with arbitrary hopping rates containing one mobile, directional impurity (defect bond). Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of Master equations lead naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasi-walker. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasi-particle through physically meaningful equations. Applications in driven diffusive systems are shown, and connections with the Duke-Rubinstein reptation models for gel electrophoresis are discussed.

cond-mat.stat-mech↗