arXiv subjects

R. K. P. Zia

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

At least 91 records · Page 5Linked to original sources

arXiv2003

Effects of differential mobility on biased diffusion of two species

Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility, and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species.

cond-mat.stat-mech↗

arXiv2002

Repeated bond traversal probabilities for the simple random walk

We consider the average number B_m(t) of bonds traversed exactly m times by a t step simple random walk. We determine B_m(t) explicitly in the scaling limit t -> oo with m/sqrt(t) fixed in dimension d=1 and m/log(t) fixed in dimension d=2. The scaling function is an erfc in d=1 and an exponential in d=2.

cond-mat.stat-mech↗

arXiv2002

Quantum Neural Networks

This paper initiates the study of quantum computing within the constraints of using a polylogarithmic ($O(\log^k n), k\geq 1$) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has focussed on using a polynomial number of qubits. A new mathematical model of computation called \emph{Quantum Neural Networks (QNNs)} is defined, building on Deutsch's model of quantum computational network. The model introduces a nonlinear and irreversible gate, similar to the speculative operator defined by Abrams and Lloyd. The precise dynamics of this operator are defined and while giving examples in which nonlinear Schrödinger's equations are applied, we speculate on its possible implementation. The many practical problems associated with the current model of quantum computing are alleviated in the new model. It is shown that QNNs of logarithmic size and constant depth have the same computational power as threshold circuits, which are used for modeling neural networks. QNNs of polylogarithmic size and polylogarithmic depth can solve the problems in \NC, the class of problems with theoretically fast parallel solutions. Thus, the new model may indeed provide an approach for building scalable parallel computers.

quant-ph↗

arXiv2001

Coarsening Dynamics of a Quasi One-dimensional Driven Lattice Gas

We study domain growth properties of two species of particles executing biased diffusion on a half-filled square lattice, consisting of just two lanes. Driven in opposite directions by an external ``electric'' field, the particles form clusters due to steric hindrance. While strictly one-dimensional systems remain disordered, clusters in our ``quasi 1D'' case grow until only a single macroscopic cluster survives. In the coarsening regime, the average cluster size increases $\sim t^{0.6}$, significantly faster than in purely diffusion-controlled systems. Remarkably, however, the cluster size distribution displays dynamic scaling, following a form consistent with a diffusion-limited growth mechanism.

cond-mat.stat-mech↗

arXiv2001

Getting More from Pushing Less: Negative Specific Heat and Conductivity in Non-equilibrium Steady States

For students familiar with equilibrium statistical mechanics, the notion of a positive specific heat, being intimately related to the idea of stability, is both intuitively reasonable and mathematically provable. However, for system in non-equilibrium stationary states, coupled to more than one energy reservoir (e.g., thermal bath), negative specific heat is entirely possible. In this paper, we present a ``minimal'' system displaying this phenomenon. Being in contact with two thermal baths at different temperatures, the (internal) energy of this system may increase when a thermostat is turned down. In another context, a similar phenomenon is negative conductivity, where a current may increase by decreasing the drive (e.g., an external electric field). The counter-intuitive behavior in both processes may be described as `` getting more from pushing less.'' The crucial ingredients for this phenomenon and the elements needed for a ``minimal'' system are also presented.

cond-mat.stat-mech↗

arXiv2001

Critical behaviour of driven bilayer systems: A field-theoretic renormalisation group study

We investigate the static and dynamic critical behaviour of a uniformly driven bilayer Ising lattice gas at half filling. Depending on the strength of the interlayer coupling J, phase separation occurs across or within the two layers. The former transitions are controlled by the universality class of model A (corresponding to an Ising model with Glauber dynamics), with upper critical dimension d_c=4. The latter transitions are dominated by the universality class of the standard (single-layer) driven Ising lattice gas, with d_c=5 and a non-classical anisotropy exponent. These two distinct critical lines meet at a non-equilibrium bicritical point which also falls into the driven Ising class. At all transitions, novel couplings and dangerous irrelevant operators determine corrections to scaling.

cond-mat.stat-mech↗

arXiv2001

Microscopic kinetics and time-dependent structure factors

The time evolution of structure factors in the disordering process of an initially phase separated lattice depends crucially on the microscopic mechanism which drives the disordering, such as Kawasaki dynamics or vacancy mediated disordering. Monte Carlo (MC) simulations show unexpected ``dips'' in the structure factors, which mean-field theory completely fails to capture. The disordering via vacancies is slower by a surprisingly large constant factor compared to Kawasaki dynamics. A phenomenological model is introduced in order to understand the dips, and an analytical solution of Kawasaki dynamics is derived, in excellent agreement with simulations. An outline is given on how to extend the analytical solution to the more complicated case of a wandering vacancy.

cond-mat.stat-mech↗

arXiv2000

A Lattice Gas Coupled to Two Thermal Reservoirs: Monte Carlo and Field Theoretic Studies

We investigate the collective behavior of an Ising lattice gas, driven to non-equilibrium steady states by being coupled to {\em two} thermal baths. Monte Carlo methods are applied to a two-dimensional system in which one of the baths is fixed at infinite temperature. Both generic long range correlations in the disordered state and critical poperties near the second order transition are measured. Anisotropic scaling, a key feature near criticality, is used to extract $T_{c}$ and some critical exponents. On the theoretical front, a continuum theory, in the spirit of Landau-Ginzburg, is presented. Being a renormalizable theory, its predictions can be computed by standard methods of $ε$-expansions and found to be consistent with simulation data. In particular, the critical behavior of this system belongs to a universality class which is quite {\em different} from the uniformly driven Ising model.

cond-mat.stat-mech↗

arXiv2000

Extremal-point Densities of Interface Fluctuations

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear Langevin equations, and for on-lattice, solid-on-solid surface growth models. We show that in spite of the non-universal character of the quantities studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic to the macroscopic observables of the system. The quantities investigated here present us with tools that give an entirely un-orthodox approach to the dynamics of surface morphologies: a statistical analysis from the short wavelength end of the Fourier decomposition spectrum. In addition to surface growth applications, our results can be used to solve the asymptotic scalability problem of massively parallel algorithms for discrete event simulations, which are extensively used in Monte-Carlo type simulations on parallel architectures.

cond-mat.stat-mech↗

arXiv2000

Fluctuations and correlations in population models with age structure

We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent death probability, as well as a variable reproduction probability for each individual as a function of age. We first solve for the steady-state of the model in mean field theory, before developing analytic techniques to compute Gaussian fluctuation corrections around the mean field fixed point. Our computations are found to be in good agreement with Monte-Carlo simulations. Finally we discuss how similar methods may be applied to fluctuations in continuous time population models.

cond-mat.stat-mech↗

arXiv1999

Viability of competing field theories for the driven lattice gas

It has recently been suggested that the driven lattice gas should be described by a novel field theory in the limit of infinite drive. We review the original and the new field theory, invoking several well-documented key features of the microscopics. Since the new field theory fails to reproduce these characteristics, we argue that it cannot serve as a viable description of the driven lattice gas. Recent results, for the critical exponents associated with this theory, are re-analyzed and shown to be incorrect.

cond-mat.stat-mech↗

arXiv1999

Dynamic scaling in vacancy-mediated disordering

We consider the disordering dynamics of an interacting binary alloy with a small admixture of vacancies which mediate atom-atom exchanges. Starting from a perfectly phase-segregated state, the system is rapidly heated to a temperature in the disordered phase. A suitable disorder parameter, namely, the number of broken bonds, is monitored as a function of time. Using Monte Carlo simulations and a coarse-grained field theory, we show that the late stages of this process exhibit dynamic scaling, characterized by a set of scaling functions and exponents. We discuss the universality of these exponents and comment on some subtleties in the early stages of the disordering process.

cond-mat.stat-mech↗

arXiv1999

Possible Existence of an Extraordinary Phase in the Driven Lattice Gas

We report recent simulation results which might indicate the existence of a new low-temperature "phase" in an Ising lattice gas, driven into a non-equilibrium steady state by an external field. It appears that this "phase", characterized by multiple-strip configurations, is selected when square systems are used to approach the thermodynamic limit. We propose a quantitative criterion for the existence of such a "phase". If confirmed, its observation may resolve a long-standing controversy over the critical properties of the driven Ising lattice gas.

cond-mat.stat-mech↗

arXiv1999

Contrasts between Equilibrium and Non-equilibrium Steady States: Computer Aided Discoveries in Simple Lattice Gases

A century ago, the foundations of equilibrium statistical mechanics were laid. For a system in equilibrium with a thermal bath, much is understood through the Boltzmann factor, exp{-H[C]/kT}, for the probability of finding the system in any microscopic configuration C. In contrast, apart from some special cases, little is known about the corresponding probabilities, if the same system is in contact with more than one reservoir of energy, so that, even in stationary states, there is a constant energy flux through our system. These non-equilibrium steady states display many surprising properties. In particular, even the simplest generalization of the Ising model offers a wealth of unexpected phenomena. Mostly discovered through Monte Carlo simulations, some of the novel properties are understood while many remain unexplained. A brief review and some recent results will be presented, highlighting the sharp contrasts between the equilibrium Ising system and this non-equilibrium counterpart.

cond-mat.stat-mech↗

arXiv1999

``Weather'' Records: Musings on Cold Days after a Long Hot Indian Summer

We present a simple, pedagogical introduction to the statistics of extreme values. Motivated by a string of record high temperatures in December 1998, we consider the distribution, averages and lifetimes for a simplified model of such ``records.'' Our ``data'' are sequences of independent random numbers all of which are generated from the same probability distribution. A remarkable universality emerges: a number of results, including the lifetime histogram, are universal, that is, independent of the underlying distribution.

cond-mat.stat-mech↗

arXiv1999

Long-Range Order in a Quasi One-Dimensional Non-Equilibrium Three-State Lattice Gas

Biased diffusion of two species with conserved dynamics on a 2xL periodic lattice is studied via Monte Carlo simulations. In contrast to its simple one-dimensional version on a ring, this quasi one-dimensional model surprisingly exhibits phase separation in its steady state, which is characterized by one macroscopic particle cluster. We study the order parameter and the cluster-size distributions as a function of the system size L, to support the above picture.

cond-mat.stat-mech↗

arXiv1998

Random Walk with a Hop-Over Site: A Novel Approach to Tagged Diffusion and Its Applications

We study, on a $d$ dimensional hypercubic lattice, a random walk which is homogeneous except for one site. Instead of visiting this site, the walker hops over it with arbitrary rates. The probability distribution of this walk and the statistics associated with the hop-overs are found exactly. This analysis provides a simple approach to the problem of tagged diffusion, i.e., the movements of a tracer particle due to the diffusion of a vacancy. Applications to vacancy mediated disordering are given through two examples.

cond-mat.stat-mech↗

arXiv1998

Three manifestations of the pulsed harmonic potential

We consider, in turn, three systems being acted upon by a regularly pulsed harmonic potential (PHP). These are i) a classical particle, ii) a quantum particle, and iii) a directed line. We contrast the mechanics of the first two systems by parameterizing their bands of stability and periodicity. Interesting differences due to quantum fluctuations are examined in detail. The fluctuations of the directed line are calculated in the two cases of a binding PHP, and an unbinding PHP. In the latter case there is a finite maximum line length for a given potential strength.

quant-ph↗