12,007 research outputs found
A study of cross sections for excitation of pseudostates
Using the electron-hydrogen scattering Temkin-Poet model we investigate the
behavior of the cross sections for excitation of all of the states used in the
convergent close-coupling (CCC) formalism. In the triplet channel, it is found
that the cross section for exciting the positive-energy states is approximately
zero near-threshold and remains so until a further energy, equal to the energy
of the state, is added to the system. This is consistent with the step-function
hypothesis [Bray, Phys. Rev. Lett. {\bf 78} 4721 (1997)] and inconsistent with
the expectations of Bencze and Chandler [Phys. Rev. A {\bf 59} 3129 (1999)].
Furthermore, we compare the results of the CCC-calculated triplet and singlet
single differential cross sections with the recent benchmark results of
Baertschy et al. [Phys. Rev. A (to be published)], and find consistent
agreement.Comment: Four pages, 5 figure
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
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
Nonequilibrium Stationary States and Phase Transitions in Directed Ising Models
We study the nonequilibrium properties of directed Ising models with non
conserved dynamics, in which each spin is influenced by only a subset of its
nearest neighbours. We treat the following models: (i) the one-dimensional
chain; (ii) the two-dimensional square lattice; (iii) the two-dimensional
triangular lattice; (iv) the three-dimensional cubic lattice. We raise and
answer the question: (a) Under what conditions is the stationary state
described by the equilibrium Boltzmann-Gibbs distribution? We show that for
models (i), (ii), and (iii), in which each spin "sees" only half of its
neighbours, there is a unique set of transition rates, namely with exponential
dependence in the local field, for which this is the case. For model (iv), we
find that any rates satisfying the constraints required for the stationary
measure to be Gibbsian should satisfy detailed balance, ruling out the
possibility of directed dynamics. We finally show that directed models on
lattices of coordination number with exponential rates cannot
accommodate a Gibbsian stationary state. We conjecture that this property
extends to any form of the rates. We are thus led to the conclusion that
directed models with Gibbsian stationary states only exist in dimension one and
two. We then raise the question: (b) Do directed Ising models, augmented by
Glauber dynamics, exhibit a phase transition to a ferromagnetic state? For the
models considered above, the answers are open problems, to the exception of the
simple cases (i) and (ii). For Cayley trees, where each spin sees only the
spins further from the root, we show that there is a phase transition provided
the branching ratio, , satisfies
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
Approach to Asymptotic Behaviour in the Dynamics of the Trapping Reaction
We consider the trapping reaction A + B -> B in space dimension d=1, where
the A and B particles have diffusion constants D_A, D_B respectively. We
calculate the probability, Q(t), that a given A particle has not yet reacted at
time t. Exploiting a recent formulation in which the B particles are eliminated
from the problem we find, for t -> \infty, , where
is the density of B particles and for .Comment: 8 pages, 2 figures; minor change
The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses
According to the droplet picture of spin glasses, the low-temperature phase
of spin glasses should be replica symmetric. However, analysis of the stability
of this state suggested that it was unstable and this instability lends support
to the Parisi replica symmetry breaking picture of spin glasses. The
finite-size scaling functions in the critical region of spin glasses below T_c
in dimensions greater than 6 can be determined and for them the replica
symmetric solution is unstable order by order in perturbation theory.
Nevertheless the exact solution can be shown to be replica-symmetric. It is
suggested that a similar mechanism might apply in the low-temperature phase of
spin glasses in less than six dimensions, but that a replica symmetry broken
state might exist in more than six dimensions.Comment: 5 pages. Modified to include a paragraph on the relation of this work
to that of Newman and Stei
Spatial fluctuations of a surviving particle in the trapping reaction
We consider the trapping reaction, , where and particles
have a diffusive dynamics characterized by diffusion constants and .
The interaction with particles can be formally incorporated in an effective
dynamics for one particle as was recently shown by Bray {\it et al}. [Phys.
Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space
dimension , the asymptotic behaviour of the spatial fluctuation,
, for a surviving particle in the perturbative regime,
, for the case of an initially uniform distribution of
particles. We show that, for , with
. By contrast, the fluctuations of paths constrained to return to
their starting point at time grow with the larger exponent 1/3. Numerical
tests are consistent with these predictions.Comment: 10 pages, 5 figure
Scaling of the Random-Field Ising Model at Zero Temperature
The exact determination of ground states of small systems is used in a
scaling study of the random-field Ising model. While three variants of the
model are found to be in the same universality class in 3 dimensions, the
Gaussian and bimodal models behave distinctly in 4 dimensions with the latter
apparently having a discontinuous jump in the magnetization. A finite-size
scaling analysis is presented for this transition.Comment: 14 pages Latex, 4 figure
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
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