174 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
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
Dynamics of Fluctuation Dominated Phase Ordering: Hard-core Passive Sliders on a Fluctuating Surface
We study the dynamics of a system of hard-core particles sliding downwards on
a one dimensional fluctuating interface, which in a special case can be mapped
to the problem of a passive scalar advected by a Burgers fluid. Driven by the
surface fluctuations, the particles show a tendency to cluster, but the
hard-core interaction prevents collapse. We use numerical simulations to
measure the auto-correlation function in steady state and in the aging regime,
and space-time correlation functions in steady state. We have also calculated
these quantities analytically in a related surface model. The steady state
auto-correlation is a scaling function of t/L^z, where L is the system size and
z the dynamic exponent. Starting from a finite intercept, the scaling function
decays with a cusp, in the small argument limit. The finite value of the
intercept indicates the existence of long range order in the system. The
space-time correlation, which is a function of r/L and t/L^z, is non-monotonic
in t for fixed r. The aging auto-correlation is a scaling function of t_1 and
t_2 where t_1 is the waiting time and t_2 the time difference. This scaling
function decays as a power law for t_2 \gg t_1; for t_1 \gg t_2, it decays with
a cusp as in steady state. To reconcile the occurrence of strong fluctuations
in the steady state with the fact of an ordered state, we measured the
distribution function of the length of the largest cluster. This shows that
fluctuations never destroy ordering, but rather the system meanders from one
ordered configuration to another on a relatively rapid time scale
Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in 2D : A study using deposition-evaporation kinetics
Deposition and evaporation of infinitely thin hard rods (needles) is studied
in two dimensions using Monte Carlo simulations. The ratio of deposition to
evaporation rates controls the equilibrium density of rods, and increasing it
leads to an entropy-driven transition to a nematic phase in which both static
and dynamical orientational correlation functions decay as power laws, with
exponents varying continuously with deposition-evaporation rate ratio. Our
results for the onset of the power-law phase agree with those for a conserved
number of rods. At a coarse-grained level, the dynamics of the non-conserved
angle field is described by the Edwards-Wilkinson equation. Predicted relations
between the exponents of the quadrupolar and octupolar correlation functions
are borne out by our numerical results. We explore the effects of spatial
inhomogeneity in the deposition-evaporation ratio by simulations, entropy-based
arguments and a study of the new terms introduced in the free energy. The
primary effect is that needles tend to align along the local spatial gradient
of the ratio. A uniform gradient thus induces a uniformly aligned state, as
does a gradient which varies randomly in magnitude and sign, but acts only in
one direction. Random variations of deposition-evaporation rates in both
directions induce frustration, resulting in a state with glassy
characteristics.Comment: modified version, Accepted for publication in Physical Review
Drift and trapping in biased diffusion on disordered lattices
We reexamine the theory of transition from drift to no-drift in biased
diffusion on percolation networks. We argue that for the bias field B equal to
the critical value B_c, the average velocity at large times t decreases to zero
as 1/log(t). For B < B_c, the time required to reach the steady-state velocity
diverges as exp(const/|B_c-B|). We propose an extrapolation form that describes
the behavior of average velocity as a function of time at intermediate time
scales. This form is found to have a very good agreement with the results of
extensive Monte Carlo simulations on a 3-dimensional site-percolation network
and moderate bias.Comment: 4 pages, RevTex, 3 figures, To appear in International Journal of
Modern Physics C, vol.
Driven k-mers: Correlations in space and time
Steady state properties of hard objects with exclusion interaction and a
driven motion along a one-dimensional periodic lattice are investigated. The
process is a generalization of the asymmetric simple exclusion process (ASEP)
to particles of length k, and is called the k-ASEP. Here, we analyze both
static and dynamic properties of the k-ASEP. Density correlations are found to
display interesting features, such as pronounced oscillations in both space and
time, as a consequence of the extended length of the particles. At long times,
the density autocorrelation decays exponentially in time, except at a special
k-dependent density when it decays as a power law. In the limit of large k at a
finite density of occupied sites, the appropriately scaled system reduces to a
nonequilibrium generalization of the Tonks gas describing the motion of hard
rods along a continuous line. This allows us to obtain in a simple way the
known two-particle distribution for the Tonks gas. For large but finite k, we
also obtain the leading-order correction to the Tonks result.Comment: 11 pages, 9 figures. Version 2: restructuring with small changes in
content, published versio
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
A complete devil's staircase in the Falicov-Kimball model
We consider the neutral, one-dimensional Falicov-Kimball model at zero
temperature in the limit of a large electron--ion attractive potential, U. By
calculating the general n-ion interaction terms to leading order in 1/U we
argue that the ground-state of the model exhibits the behavior of a complete
devil's staircase.Comment: 6 pages, RevTeX, 3 Postscript figure
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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