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 $g(0)$, in both three dimensions and two dimensions. Furthermore, we prove, in general, the ladder theory satisfies the cusp condition for the pair-correlation density $g(r)$ at zero distance $r=0$.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 $\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that is in agreement with well known scaling arguments.Comment: 4 page