19,293 research outputs found
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
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
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 where 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
Diffusion of active tracers in fluctuating fields
The problem of a particle diffusion in a fluctuating scalar field is studied.
In contrast to most studies of advection diffusion in random fields we analyze
the case where the particle position is also coupled to the dynamics of the
field. Physical realizations of this problem are numerous and range from the
diffusion of proteins in fluctuating membranes and the diffusion of localized
magnetic fields in spin systems. We present exact results for the diffusion
constant of particles diffusing in dynamical Gaussian fields in the adiabatic
limit where the field evolution is much faster than the particle diffusion. In
addition we compute the diffusion constant perturbatively, in the weak coupling
limit where the interaction of the particle with the field is small, using a
Kubo-type relation. Finally we construct a simple toy model which can be solved
exactly.Comment: 13 pages, 1 figur
Density Dependence of the Mass Function of Globular Star Clusters in the Sombrero Galaxy and its Dynamical Implications
We have constructed the mass function of globular star clusters in the
Sombrero galaxy in bins of different internal half-mass density rho_h and
projected galactocentric distance R. This is based on the published
measurements of the magnitudes and effective radii of the clusters by Spitler
et al. (2006) in BVR images taken with the ACS on HST. We find that the peak of
the mass function M_p increases with rho_h by a factor of about 4 but remains
nearly constant with R. Our results are almost identical to those presented
recently by McLaughlin & Fall (2007) for globular clusters in the Milky Way.
The mass functions in both galaxies agree with a simple, approximate model in
which the clusters form with a Schechter initial mass function and evolve
subsequently by stellar escape driven by internal two-body relaxation. These
findings therefore undermine recent claims that the present peak of the mass
function of globular clusters must have been built into the initial conditions.Comment: Astrophysical Journal Letters, in press. 4 page
Shell Model Monte Carlo Methods
We review quantum Monte Carlo methods for dealing with large shell model
problems. These methods reduce the imaginary-time many-body evolution operator
to a coherent superposition of one-body evolutions in fluctuating one-body
fields; the resultant path integral is evaluated stochastically. We first
discuss the motivation, formalism, and implementation of such Shell Model Monte
Carlo (SMMC) methods. There then follows a sampler of results and insights
obtained from a number of applications. These include the ground state and
thermal properties of {\it pf}-shell nuclei, the thermal and rotational
behavior of rare-earth and -soft nuclei, and the calculation of double
beta-decay matrix elements. Finally, prospects for further progress in such
calculations are discussed
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 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
- …