12,890 research outputs found
Calculation of the free-free transitions in the electron-hydrogen scattering S-wave model
The S-wave model of electron-hydrogen scattering is evaluated using the
convergent close-coupling method with an emphasis on scattering from excited
states including an initial state from the target continuum. Convergence is
found for discrete excitations and the elastic free-free transition. The latter
is particularly interesting given the corresponding potential matrix elements
are divergent
Survival of a diffusing particle in an expanding cage
We consider a Brownian particle, with diffusion constant D, moving inside an
expanding d-dimensional sphere whose surface is an absorbing boundary for the
particle. The sphere has initial radius L_0 and expands at a constant rate c.
We calculate the joint probability density, p(r,t|r_0), that the particle
survives until time t, and is at a distance r from the centre of the sphere,
given that it started at a distance r_0 from the centre.Comment: 5 page
Corrections to Scaling in Phase-Ordering Kinetics
The leading correction to scaling associated with departures of the initial
condition from the scaling morphology is determined for some soluble models of
phase-ordering kinetics. The result for the pair correlation function has the
form C(r,t) = f_0(r/L) + L^{-\omega} f_1(r/L) + ..., where L is a
characteristic length scale extracted from the energy. The
correction-to-scaling exponent \omega has the value \omega=4 for the d=1
Glauber model, the n-vector model with n=\infty, and the approximate theory of
Ohta, Jasnow and Kawasaki. For the approximate Mazenko theory, however, \omega
has a non-trivial value: omega = 3.8836... for d=2, and \omega = 3.9030... for
d=3. The correction-to-scaling functions f_1(x) are also calculated.Comment: REVTEX, 7 pages, two figures, needs epsf.sty and multicol.st
On the number of metastable states in spin glasses
In this letter, we show that the formulae of Bray and Moore for the average
logarithm of the number of metastable states in spin glasses can be obtained by
calculating the partition function with coupled replicas with the symmetry
among these explicitly broken according to a generalization of the `two-group'
ansatz. This equivalence allows us to find solutions of the BM equations where
the lower `band-edge' free energy equals the standard static free energy. We
present these results for the Sherrington-Kirkpatrick model, but we expect them
to apply to all mean-field spin glasses.Comment: 6 pages, LaTeX, no figures. Postscript directly available
http://chimera.roma1.infn.it/index_papers_complex.htm
Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey
We consider a system of three random walkers (a `cheetah' surrounded by two
`antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse,
but the antelopes experience in addition a deterministic relative drift
velocity, away from the cheetah, proportional to their distance from the
cheetah, such that they tend to move away from the cheetah with increasing
time. Using the backward Fokker-Planck equation we calculate, as a function of
their initial separations, the probability that the cheetah has caught neither
antelope after infinite time.Comment: 5 page
Persistence and the Random Bond Ising Model in Two Dimensions
We study the zero-temperature persistence phenomenon in the random bond Ising model on a square lattice via extensive numerical simulations. We find
strong evidence for ` blocking\rq regardless of the amount disorder present in
the system. The fraction of spins which {\it never} flips displays interesting
non-monotonic, double-humped behaviour as the concentration of ferromagnetic
bonds is varied from zero to one. The peak is identified with the onset of
the zero-temperature spin glass transition in the model. The residual
persistence is found to decay algebraically and the persistence exponent
over the range . Our results are
completely consistent with the result of Gandolfi, Newman and Stein for
infinite systems that this model has ` mixed\rq behaviour, namely positive
fractions of spins that flip finitely and infinitely often, respectively.
[Gandolfi, Newman and Stein, Commun. Math. Phys. {\bf 214} 373, (2000).]Comment: 9 pages, 5 figure
Spin-resolved electron-impact ionization of lithium
Electron-impact ionization of lithium is studied using the convergent
close-coupling (CCC) method at 25.4 and 54.4 eV. Particular attention is paid
to the spin-dependence of the ionization cross sections. Convergence is found
to be more rapid for the spin asymmetries, which are in good agreement with
experiment, than for the underlying cross sections. Comparison with the recent
measured and DS3C-calculated data of Streun et al (1999) is most intriguing.
Excellent agreement is found with the measured and calculated spin asymmetries,
yet the discrepancy between the CCC and DS3C cross sections is very large
Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results
We consider the pair correlation functions of both the order parameter field
and its square for phase ordering in the model with nonconserved order
parameter, in spatial dimension and spin dimension .
We calculate, in the scaling limit, the exact short-distance singularities of
these correlation functions and compare these predictions to numerical
simulations. Our results suggest that the scaling hypothesis does not hold for
the model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
Non-equilibrium Phase-Ordering with a Global Conservation Law
In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising
model leads to an asymptotic length-scale
at because the kinetic coefficient is renormalized by the broken-bond
density, . For , activated kinetics recovers the
standard asymptotic growth-law, . However, at all temperatures,
infinite-range energy-transport is allowed by the spin-exchange dynamics. A
better implementation of global conservation, the microcanonical Creutz
algorithm, is well behaved and exhibits the standard non-conserved growth law,
, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st
Global Persistence Exponent for Critical Dynamics
A `persistence exponent' is defined for nonequilibrium critical
phenomena. It describes the probability, , that the
global order parameter has not changed sign in the time interval following
a quench to the critical point from a disordered state. This exponent is
calculated in mean-field theory, in the limit of the model,
to first order in , and for the 1-d Ising model. Numerical
results are obtained for the 2-d Ising model. We argue that is a new
independent exponent.Comment: 4 pages, revtex, one figur
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