278 research outputs found
The on-top pair-correlation density in the homogeneous electron liquid
The ladder theory, in which the Bethe-Goldstone equation for the effective
potential between two scattering particles plays a central role, is well known
for its satisfactory description of the short-range correlations in the
homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in
the limit of large transfer momentum between two scattering particles, we
obtain accurate results for the on-top pair-correlation density , in both
three dimensions and two dimensions. Furthermore, we prove, in general, the
ladder theory satisfies the cusp condition for the pair-correlation density
at zero distance .Comment: 8 pages, 4 figure
Pair densities at contact in the quantum electron gas
The value of the pair distribution function g(r) at contact (r = 0) in a
quantum electron gas is determined by the scattering events between pairs of
electrons with antiparallel spins. The theoretical results for g(0) as a
function of the coupling strength r_s in the paramagnetic electron gas in
dimensionality D=2 and 3, that have been obtained from the solution of the
two-body scattering problem with a variety of effective scattering potentials
embodying many-body effects, are compared with the results of many-body
calculations in the ladder approximation and with quantum Monte Carlo data.Comment: 7 pages, 2 figure
Model of Cluster Growth and Phase Separation: Exact Results in One Dimension
We present exact results for a lattice model of cluster growth in 1D. The
growth mechanism involves interface hopping and pairwise annihilation
supplemented by spontaneous creation of the stable-phase, +1, regions by
overturning the unstable-phase, -1, spins with probability p. For cluster
coarsening at phase coexistence, p=0, the conventional structure-factor scaling
applies. In this limit our model falls in the class of diffusion-limited
reactions A+A->inert. The +1 cluster size grows diffusively, ~t**(1/2), and the
two-point correlation function obeys scaling. However, for p>0, i.e., for the
dynamics of formation of stable phase from unstable phase, we find that
structure-factor scaling breaks down; the length scale associated with the size
of the growing +1 clusters reflects only the short-distance properties of the
two-point correlations.Comment: 12 page
Transport on Directed Percolation Clusters
We study random lattice networks consisting of resistor like and diode like
bonds. For investigating the transport properties of these random resistor
diode networks we introduce a field theoretic Hamiltonian amenable to
renormalization group analysis. We focus on the average two-port resistance at
the transition from the nonpercolating to the directed percolating phase and
calculate the corresponding resistance exponent to two-loop order.
Moreover, we determine the backbone dimension of directed percolation
clusters to two-loop order. We obtain a scaling relation for that is in
agreement with well known scaling arguments.Comment: 4 page
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