301 research outputs found
Numerical Diagonalisation Study of the Trimer Deposition-Evaporation Model in One Dimension
We study the model of deposition-evaporation of trimers on a line recently
introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the
model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain
with three-spin couplings given by H= \sum\displaylimits_i [(1 -
\sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+
+ h.c]. We study by exact numerical diagonalization of the variation of
the gap in the eigenvalue spectrum with the system size for rings of size up to
30. For the sector corresponding to the initial condition in which all sites
are empty, we find that the gap vanishes as where the gap exponent
is approximately . This model is equivalent to an interfacial
roughening model where the dynamical variables at each site are matrices. From
our estimate for the gap exponent we conclude that the model belongs to a new
universality class, distinct from that studied by Kardar, Parisi and Zhang.Comment: 11 pages, 2 figures (included
Dynamics of a disordered, driven zero range process in one dimension
We study a driven zero range process which models a closed system of
attractive particles that hop with site-dependent rates and whose steady state
shows a condensation transition with increasing density. We characterise the
dynamical properties of the mass fluctuations in the steady state in one
dimension both analytically and numerically and show that the transport
properties are anomalous in certain regions of the density-disorder plane. We
also determine the form of the scaling function which describes the growth of
the condensate as a function of time, starting from a uniform density
distribution.Comment: Revtex4, 5 pages including 2 figures; Revised version; To appear in
Phys. Rev. Let
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.Comment: 39 pages, with 5 eps figures, to appear in J. Stat. Phys. (March
1997
Dynamics of Shock Probes in Driven Diffusive Systems
We study the dynamics of shock-tracking probe particles in driven diffusive
systems and also in equilibrium systems. In a driven system, they induce a
diverging timescale that marks the crossover between a passive scalar regime at
early times and a diffusive regime at late times; a scaling form characterises
this crossover. Introduction of probes into an equilibrium system gives rise to
a system-wide density gradient, and the presence of even a single probe can be
felt across the entire system.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen
Directed diffusion of reconstituting dimers
We discuss dynamical aspects of an asymmetric version of assisted diffusion
of hard core particles on a ring studied by G. I. Menon {\it et al.} in J. Stat
Phys. {\bf 86}, 1237 (1997). The asymmetry brings in phenomena like kinematic
waves and effects of the Kardar-Parisi-Zhang nonlinearity, which combine with
the feature of strongly broken ergodicity, a characteristic of the model. A
central role is played by a single nonlocal invariant, the irreducible string,
whose interplay with the driven motion of reconstituting dimers, arising from
the assisted hopping, determines the asymptotic dynamics and scaling regimes.
These are investigated both analytically and numerically through
sector-dependent mappings to the asymmetric simple exclusion process.Comment: 10 pages, 6 figures. Slight corrections, one added reference. To
appear in J. Phys. Cond. Matt. (2007). Special issue on chemical kinetic
Finite-size effects on the dynamics of the zero-range process
We study finite-size effects on the dynamics of a one-dimensional zero-range
process which shows a phase transition from a low-density disordered phase to a
high-density condensed phase. The current fluctuations in the steady state show
striking differences in the two phases. In the disordered phase, the variance
of the integrated current shows damped oscillations in time due to the motion
of fluctuations around the ring as a dissipating kinematic wave. In the
condensed phase, this wave cannot propagate through the condensate, and the
dynamics is dominated by the long-time relocation of the condensate from site
to site.Comment: 5 pages, 5 figures, version published in Phys. Rev. E Rapid
Communication
Anomaly in the relaxation dynamics close to the surface plasmon resonance
We propose an explanation for the anomalous behaviour observed in the
relaxation dynamics of the differential optical transmission of noble-metal
nanoparticles. Using the temperature dependences of the position and the width
of the surface plasmon resonance, we obtain a strong frequency dependence in
the time evolution of the transmission close to the resonance. In particular,
our approach accounts for the slowdown found below the plasmon frequency. This
interpretation is independent of the presence of a nearby interband transition
which has been invoked previously. We therefore argue that the anomaly should
also appear for alkaline nanoparticles.Comment: version published in EP
The Irreducible String and an Infinity of Additional Constants of Motion in a Deposition-Evaporation Model on a Line
We study a model of stochastic deposition-evaporation with recombination, of
three species of dimers on a line. This model is a generalization of the model
recently introduced by Barma {\it et. al.} (1993 {\it Phys. Rev. Lett.} {\bf
70} 1033) to states per site. It has an infinite number of constants
of motion, in addition to the infinity of conservation laws of the original
model which are encoded as the conservation of the irreducible string. We
determine the number of dynamically disconnected sectors and their sizes in
this model exactly. Using the additional symmetry we construct a class of exact
eigenvectors of the stochastic matrix. The autocorrelation function decays with
different powers of in different sectors. We find that the spatial
correlation function has an algebraic decay with exponent 3/2, in the sector
corresponding to the initial state in which all sites are in the same state.
The dynamical exponent is nontrivial in this sector, and we estimate it
numerically by exact diagonalization of the stochastic matrix for small sizes.
We find that in this case .Comment: Some minor errors in the first version has been correcte
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.Comment: 4 pages, RevTeX, 4 eps figures included using 'psfig.sty
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- 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.Comment: RevTex, 17pages, 18 figures included using psfig.st
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