arXiv subjects

Mustansir Barma

Publications and source records attributed to Mustansir Barma.

80 records · Page 5Linked to original sources

arXiv1997

Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes

We study the effect of quenched spatial disorder on the steady states of driven systems of interacting particles. Two sorts of models are studied: disordered drop-push processes and their generalizations, and the disordered asymmetric simple exclusion process. We write down the exact steady-state measure, and consequently a number of physical quantities explicitly, for the drop-push dynamics in any dimensions for arbitrary disorder. We find that three qualitatively different regimes of behaviour are possible in 1-$d$ disordered driven systems. In the Vanishing-Current regime, the steady-state current approaches zero in the thermodynamic limit. A system with a non-zero current can either be in the Homogeneous regime, chracterized by a single macroscopic density, or the Segregated-Density regime, with macroscopic regions of different densities. We comment on certain important constraints to be taken care of in any field theory of disordered systems.

cond-mat.stat-mech↗

arXiv1997

Phase Transition in a Conserved-Mass Model of Aggregation and Dissociation

We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a striking behaviour in the steady state. As the parameters are varied, the system undergoes a dynamical phase transition in all dimensions. In one phase the mass distribution decays exponentially for large mass whereas in the other phase there is a power law distribution of masses which coexists with an infinite mass aggregate. The model is investigated analytically within mean field theory, and numerically in one dimension.

cond-mat.stat-mech↗

arXiv1997

Steady State and Dynamics of Driven Diffusive Systems with Quenched Disorder

We study the effect of quenched disorder on nonequilibrium systems of interacting particles, specifically, driven diffusive lattice gases with spatially disordered jump rates. The exact steady-state measure is found for a class of models evolving by drop-push dynamics, allowing several physical quantities to be calculated. Dynamical correlations are studied numerically in one dimension. We conjecture that the relevance of quenched disorder depends crucially upon the speed of the kinematic waves in the system. Time-dependent correlation functions, which monitor the dissipation of kinematic waves, behave as in pure system if the wave speed is non-zero. When the wave speed vanishes, e.g. for the disordered exclusion process close to half filling, disorder is strongly relevant and induces separation of phases with different macroscopic densities. In this case the exponent characterizing the dynamical correlation function changes.

cond-mat.dis-nn↗

arXiv1997

Conservation Laws and Integrability of a One-dimensional Model of Diffusing Dimers

We study a model of assisted diffusion of hard-core particles on a line. The model shows strongly ergodicity breaking : configuration space breaks up into an exponentially large number of disconnected sectors. We determine this sector-decomposion exactly. Within each sector the model is reducible to the simple exclusion process, and is thus equivalent to the Heisenberg model and is fully integrable. We discuss additional symmetries of the equivalent quantum Hamiltonian which relate observables in different sectors. In some sectors, the long-time decay of correlation functions is qualitatively different from that of the simple exclusion process. These decays in different sectors are deduced from an exact mapping to a model of the diffusion of hard-core random walkers with conserved spins, and are also verified numerically. We also discuss some implications of the existence of an infinity of conservation laws for a hydrodynamic description.

cond-mat.stat-mech↗

arXiv1996

Active-Site Motion and Pattern Formation in Self-Organised Interface Depinning

We study a dynamically generated pattern in height gradients, centered around the active growth site, in the steady state of a self-organised interface depinning model. The pattern has a power-law tail and depends on interface slope. An approximate integral equation relates the profile to local interface readjustments and long-ranged jumps of the active site. The pattern results in a two-point correlation function saturating to a finite value which depends on system size. Pattern formation is generic to systems in which the dynamics leads to correlated motion of the active site.

cond-mat↗

arXiv1995

Resonances in Small Fermi Systems

The systematics of the size dependence of the resonant response of small metal particles and nuclei to incident electromagnetic radiation is studied. The known radius$^{-1}$ variation of the full width at half maximum (FWHM) in matrix-embedded metal particles is qualitatively accounted for by a quantum calculation of the response within a simple model. In free clusters, the behaviour is more complicated, possibly because of thermal excitation of surface modes. For nuclei, the FWHM shows strong shell-structure-linked oscillations across the periodic table. Focussing on the lower envelope of the oscillations (magic nuclei), the downward trend of the FWHM is consistent with the radius$^{-1}$ variation. A schematic theoretical description of the systematics in nuclei is presented. If the FWHMs are scaled by the respective Fermi energies and the inverse radii by the Fermi wave vectors, the data sets for matrix-embedded metal particles and nuclei become comparable in magnitude.

cond-mat↗

arXiv1994

Slow Relaxation in a Model with Many Conservation Laws : Deposition and Evaporation of Trimers on a Line

We study the slow decay of the steady-state autocorrelation function $C(t)$ in a stochastic model of deposition and evaporation of trimers on a line with infinitely many conservation laws and sectors. Simulations show that $C(t)$ decays as different powers of $t$, or as $\exp (-t^{1/2})$, depending on the sector. We explain this diversity by relating the problem to diffusion of hard core particles with conserved spin labels. The model embodies a matrix generalization of the Kardar-Parisi-Zhang model of interface roughening. In the sector which includes the empty line, the dynamical exponent $z$ is $2.55 \pm 0.15$.

cond-mat↗

arXiv1992

Random Sequential Adsorption on a Line: Mean-Field Theory of Diffusional Relaxation

We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes and is valid over a significantly larger range than an earlier variant, which was based on a mapping to chemical reactions. In particular, continuum-limit off-lattice deposition is described naturally within our approximation. The criteria for the applicability of the mean-field theory are derived. While deposition of dimers, and marginally, trimers, is affected by fluctuations, we find that the k-mer deposition kinetics is asymptotically mean-field like for all k=4,5,..., where the limit k->infinity, when properly defined, describes deposition-diffusion kinetics in the continuum.

cond-mat↗