21,130 research outputs found

### Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and
effective drift of a particle moving in a random medium. The velocity of the
particle combines a white noise diffusion process with a local drift term that
depends linearly on the gradient of a gaussian random field with homogeneous
statistics. The theoretical analysis is confirmed by numerical simulation. For
the purely isotropic case the simulation, which measures the effective drift
directly in a constant gradient background field, confirms the result
previously obtained theoretically, that the effective diffusivity and effective
drift are renormalized by the same factor from their local values. For this
isotropic case we provide an intuitive explanation, based on a {\it spatial}
average of local drift, for the renormalization of the effective drift
parameter relative to its local value. We also investigate situations in which
the isotropy is broken by the tensorial relationship of the local drift to the
gradient of the random field. We find that the numerical simulation confirms a
relatively simple renormalization group calculation for the effective
diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep

### Metastable states of spin glasses on random thin graphs

In this paper we calculate the mean number of metastable states for spin
glasses on so called random thin graphs with couplings taken from a symmetric
binary distribution $\pm J$. Thin graphs are graphs where the local
connectivity of each site is fixed to some value $c$. As in totally connected
mean field models we find that the number of metastable states increases
exponentially with the system size. Furthermore we find that the average number
of metastable states decreases as $c$ in agreement with previous studies
showing that finite connectivity corrections of order $1/c$ increase the number
of metastable states with respect to the totally connected mean field limit. We
also prove that the average number of metastable states in the limit
$c\to\infty$ is finite and converges to the average number of metastable states
in the Sherrington-Kirkpatrick model. An annealed calculation for the number of
metastable states $N_{MS}(E)$ of energy $E$ is also carried out giving a lower
bound on the ground state energy of these spin glasses. For small $c$ one may
obtain analytic expressions for $$.Comment: 13 pages LateX, 3 figures .ep

### Dynamical transition for a particle in a squared Gaussian potential

We study the problem of a Brownian particle diffusing in finite dimensions in
a potential given by $\psi= \phi^2/2$ where $\phi$ is Gaussian random field.
Exact results for the diffusion constant in the high temperature phase are
given in one and two dimensions and it is shown to vanish in a power-law
fashion at the dynamical transition temperature. Our results are confronted
with numerical simulations where the Gaussian field is constructed, in a
standard way, as a sum over random Fourier modes. We show that when the number
of Fourier modes is finite the low temperature diffusion constant becomes
non-zero and has an Arrhenius form. Thus we have a simple model with a fully
understood finite size scaling theory for the dynamical transition. In addition
we analyse the nature of the anomalous diffusion in the low temperature regime
and show that the anomalous exponent agrees with that predicted by a trap
model.Comment: 18 pages, 4 figures .eps, JPA styl

### Path integrals for stiff polymers applied to membrane physics

Path integrals similar to those describing stiff polymers arise in the
Helfrich model for membranes. We show how these types of path integrals can be
evaluated and apply our results to study the thermodynamics of a minority
stripe phase in a bulk membrane. The fluctuation induced contribution to the
line tension between the stripe and the bulk phase is computed, as well as the
effective interaction between the two phases in the tensionless case where the
two phases have differing bending rigidities.Comment: 11 pages RevTex, 4 figure

### Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two
dimensional Langevin tracer particle in the force field generated by charged
point scatterers with quenched positions. We show that if the point scatterers
have a screened Coulomb (Yukawa) potential and are uniformly and independently
distributed then the effective diffusion constant obeys the
Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained
for pure Coulomb scatterers frozen in an equilibrium configuration of the same
temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

### Some observations on the renormalization of membrane rigidity by long-range interactions

We consider the renormalization of the bending and Gaussian rigidity of model
membranes induced by long-range interactions between the components making up
the membrane. In particular we analyze the effect of a finite membrane
thickness on the renormalization of the bending and Gaussian rigidity by
long-range interactions. Particular attention is paid to the case where the
interactions are of a van der Waals type.Comment: 11 pages RexTex, no figure

### Perturbation theory for the effective diffusion constant in a medium of random scatterer

We develop perturbation theory and physically motivated resummations of the
perturbation theory for the problem of a tracer particle diffusing in a random
media. The random media contains point scatterers of density $\rho$ uniformly
distributed through out the material. The tracer is a Langevin particle
subjected to the quenched random force generated by the scatterers. Via our
perturbative analysis we determine when the random potential can be
approximated by a Gaussian random potential. We also develop a self-similar
renormalisation group approach based on thinning out the scatterers, this
scheme is similar to that used with success for diffusion in Gaussian random
potentials and agrees with known exact results. To assess the accuracy of this
approximation scheme its predictions are confronted with results obtained by
numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style

### Calculation of exciton densities in SMMC

We develop a shell-model Monte Carlo (SMMC) method to calculate densities of
states with varying exciton (particle-hole) number. We then apply this method
to the doubly closed-shell nucleus 40Ca in a full 0s-1d-0f-1p shell-model space
and compare our results to those found using approximate analytic expressions
for the partial densities. We find that the effective one-body level density is
reduced by approximately 22% when a residual two-body interaction is included
in the shell model calculation.Comment: 10 pages, 4 figure

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