32 research outputs found
Single-Particle Diffusion-Coefficient on Surfaces with Ehrlich-Schwoebel-Barriers
The diffusion coefficient of single particles in the presence of
Ehrlich-Schwoebel barriers (ESB)is considered. An exact expression is given for
the diffusion coefficient on linear chains with random arrangements of ESB. The
results are extended to surfaces having ESB with uniform extension in one or
both directions. All results are verified by Monte Carlo simulations.Comment: 11 pages, LaTeX2e, 6 eps-figure
Longitudinal spin relaxation in simple stochastic models for disordered systems
The relaxation of single probe spins was investigated for simple models of systems with quenched disorder. The spin relaxation was calculated for a two-site model with arbitrarily oriented magnetic fields and the result was averaged over various distributions of the fields, and of the hopping rates of the spin. On an intermediate time scale, a modified Kubo-Toyabe behavior is obtained for large hopping rates, in agreement with recent SR experiments. A stretched-exponential decay of the spin polarization is obtained at longer times. The Kohlrausch exponent is found to be field and hopping-rate dependent, in qualitative agreement with recent NMR and -NMR experiments. The resulting longitudinal relaxation rate still does not show the significant deviations from the Bloembergen-Purcell-Pound (BPP) behavior that are typical for glassy systems. Therefore, the random two-frequency model was extended to include time-dependent renewals of the environment. This modification may yield asymmetric peaks for the longitudinal relaxation rate in the BPP plot for very large renewal rates. © 1995 The American Physical Society
Hopping motion of lattice gases through nonsymmetric potentials under strong bias conditions
The hopping motion of lattice gases through potentials without
mirror-reflection symmetry is investigated under various bias conditions. The
model of 2 particles on a ring with 4 sites is solved explicitly; the resulting
current in a sawtooth potential is discussed. The current of lattice gases in
extended systems consisting of periodic repetitions of segments with sawtooth
potentials is studied for different concentrations and values of the bias.
Rectification effects are observed, similar to the single-particle case. A
mean-field approximation for the current in the case of strong bias acting
against the highest barriers in the system is made and compared with numerical
simulations. The particle-vacancy symmetry of the model is discussed.Comment: 8 pages (incl. 6 eps figures); RevTeX 3.
Absence of self-averaging in the complex admittance for transport through random media
A random walk model in a one dimensional disordered medium with an
oscillatory input current is presented as a generic model of boundary
perturbation methods to investigate properties of a transport process in a
disordered medium. It is rigorously shown that an admittance which is equal to
the Fourier-Laplace transform of the first-passage time distribution is
non-self-averaging when the disorder is strong. The low frequency behavior of
the disorder-averaged admittance, where , does not coincide with the low frequency behavior of the admittance for any
sample, . It implies that the Cole-Cole plot of
appears at a different position from the Cole-Cole plots of of any
sample. These results are confirmed by Monte-Carlo simulations.Comment: 7 pages, 2 figures, published in Phys. Rev.
Continuum theory of vacancy-mediated diffusion
We present and solve a continuum theory of vacancy-mediated diffusion (as
evidenced, for example, in the vacancy driven motion of tracers in crystals).
Results are obtained for all spatial dimensions, and reveal the strongly
non-gaussian nature of the tracer fluctuations. In integer dimensions, our
results are in complete agreement with those from previous exact lattice
calculations. We also extend our model to describe the vacancy-driven
fluctuations of a slaved flux line.Comment: 25 Latex pages, subm. to Physical Review
Lattice gas model in random medium and open boundaries: hydrodynamic and relaxation to the steady state
We consider a lattice gas interacting by the exclusion rule in the presence
of a random field given by i.i.d. bounded random variables in a bounded domain
in contact with particles reservoir at different densities. We show, in
dimensions , that the rescaled empirical density field almost surely,
with respect to the random field, converges to the unique weak solution of a
non linear parabolic equation having the diffusion matrix determined by the
statistical properties of the external random field and boundary conditions
determined by the density of the reservoir. Further we show that the rescaled
empirical density field, in the stationary regime, almost surely with respect
to the random field, converges to the solution of the associated stationary
transport equation
Motion of a driven tracer particle in a one-dimensional symmetric lattice gas
We study the dynamics of a tracer particle subject to a constant driving
force in a one-dimensional lattice gas of hard-core particles whose
transition rates are symmetric. We show that the mean displacement of the
driven tracer grows in time, , as , rather than the linear
time dependence found for driven diffusion in the bath of non-interacting
(ghost) particles. The prefactor is determined implicitly, as the
solution of a transcendental equation, for an arbitrary magnitude of the
driving force and an arbitrary concentration of the lattice gas particles. In
limiting cases the prefactor is obtained explicitly. Analytical predictions are
seen to be in a good agreement with the results of numerical simulations.Comment: 21 pages, LaTeX, 4 Postscript fugures, to be published in Phys. Rev.
E, (01Sep, 1996
Hopping Transport in the Presence of Site Energy Disorder: Temperature and Concentration Scaling of Conductivity Spectra
Recent measurements on ion conducting glasses have revealed that conductivity
spectra for various temperatures and ionic concentrations can be superimposed
onto a common master curve by an appropriate rescaling of the conductivity and
frequency. In order to understand the origin of the observed scaling behavior,
we investigate by Monte Carlo simulations the diffusion of particles in a
lattice with site energy disorder for a wide range of both temperatures and
concentrations. While the model can account for the changes in ionic activation
energies upon changing the concentration, it in general yields conductivity
spectra that exhibit no scaling behavior. However, for typical concentrations
and sufficiently low temperatures, a fairly good data collapse is obtained
analogous to that found in experiment.Comment: 6 pages, 4 figure
Survival and residence times in disordered chains with bias
We present a unified framework for first-passage time and residence time of
random walks in finite one-dimensional disordered biased systems. The
derivation is based on exact expansion of the backward master equation in
cumulants. The dependence on initial condition, system size, and bias strength
is explicitly studied for models with weak and strong disorder. Application to
thermally activated processes is also developed.Comment: 13 pages with 2 figures, RevTeX4; v2:minor grammatical changes, typos
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