Velocity Distribution of Topological Defects in Phase-Ordering Systems

The distribution of interface (domain-wall) velocities ${\bf v}$ in a phase-ordering system is considered. Heuristic scaling arguments based on the disappearance of small domains lead to a power-law tail, $P_v(v) \sim v^{-p}$ for large v, in the distribution of $v \equiv |{\bf v}|$. The exponent p is given by $p = 2+d/(z-1)$, where d is the space dimension and 1/z is the growth exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to systems described by a vector order parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear in Physical Review E (May 1, 1997

Scaling Model of Annihilation-Diffusion Kinetics for Charged Particles with Long-Range Interactions

We propose the general scaling model for the diffusio n-annihilation reaction $A_{+} + A_{-} \longrightarrow \emptyset$ with long-range power-law i nteractions. The presented scaling arguments lead to the finding of three different regimes, dep ending on the space dimensionality d and the long-range force power e xponent n. The obtained kinetic phase diagram agrees well with existing simulation data and approximate theoretical results.Comment: RevTEX, 7 pages, no figures, accepted to Physical Review

Renormalization group and perfect operators for stochastic differential equations

We develop renormalization group methods for solving partial and stochastic differential equations on coarse meshes. Renormalization group transformations are used to calculate the precise effect of small scale dynamics on the dynamics at the mesh size. The fixed point of these transformations yields a perfect operator: an exact representation of physical observables on the mesh scale with minimal lattice artifacts. We apply the formalism to simple nonlinear models of critical dynamics, and show how the method leads to an improvement in the computational performance of Monte Carlo methods.Comment: 35 pages, 16 figure

W_\infty and w_\infty Gauge Theories and Contraction

We present a general method of constructing Winf and winf gauge theories in terms of d+2 dimensional local fields. In this formulation the \Winf gauge theory Lagrangians involve non-local interactions, but the winf theories are entirely local. We discuss the so-called classical contraction procedure by which we derive the Lagrangian of winf gauge theory from that of the corresponding Winf gauge theory. In order to discuss the relationship between quantum Winf and quantum winf gauge theory we solve d=1 gauge theory models of a Higgs field exactly by using the collective field method. Based on this we conclude that the Winf gauge theory can be regarded as the large N limit of the corresponding SU(N) gauge theory once an appropriate coupling constant renormalization is made, while the winf gauge theory cannot be.Comment: 21 pages, plain Te

Dynamics of orientational ordering in fluid membranes

We study the dynamics of orientational phase ordering in fluid membranes. Through numerical simulation we find an unusually slow coarsening of topological texture, which is limited by subdiffusive propagation of membrane curvature. The growth of the orientational correlation length $\xi$ obeys a power law $\xi \propto t^w$ with $w < 1/4$ in the late stage. We also discuss defect profiles and correlation patterns in terms of long-range interaction mediated by curvature elasticity.Comment: 5 pages, 3 figures (1 in color); Eq.(9) correcte

Relaxation and Coarsening Dynamics in Superconducting Arrays

We investigate the nonequilibrium coarsening dynamics in two-dimensional overdamped superconducting arrays under zero external current, where ohmic dissipation occurs on junctions between superconducting islands through uniform resistance. The nonequilibrium relaxation of the unfrustrated array and also of the fully frustrated array, quenched to low temperature ordered states or quasi-ordered ones, is dominated by characteristic features of coarsening processes via decay of point and line defects, respectively. In the case of unfrustrated arrays, it is argued that due to finiteness of the friction constant for a vortex (in the limit of large spatial extent of the vortex), the typical length scale grows as $\ell_s \sim t^{1/2}$ accompanied by the number of point vortices decaying as $N_v \sim 1/t$. This is in contrast with the case that dominant dissipation occurs between each island and the substrate, where the friction constant diverges logarithmically and the length scale exhibits diffusive growth with a logarithmic correction term. We perform extensive numerical simulations, to obtain results in reasonable agreement. In the case of fully frustrated arrays, the domain growth of Ising-like chiral order exhibits the low-temperature behavior $\ell_q \sim t^{1/z_q}$, with the growth exponent $1/z_q$ apparently showing a strong temperature dependence in the low-temperature limit.Comment: 9 pages, 5 figures, to be published in Phys. Rev.

Growth Laws for Phase Ordering

We determine the characteristic length scale, $L(t)$, in phase ordering kinetics for both scalar and vector fields, with either short- or long-range interactions, and with or without conservation laws. We obtain $L(t)$ consistently by comparing the global rate of energy change to the energy dissipation from the local evolution of the order parameter. We derive growth laws for O(n) models, and our results can be applied to other systems with similar defect structures.Comment: 12 pages, LaTeX, second tr

Estimation of vortex density after superconducting film quench

This paper addresses the problem of vortex formation during a rapid quench in a superconducting film. It builds on previous work showing that in a local gauge theory there are two distinct mechanisms of defect formation, based on fluctuations of the scalar and gauge fields, respectively. We show how vortex formation in a thin film differs from the fully two-dimensional case, on which most theoretical studies have focused. We discuss ways of testing theoretical predictions in superconductor experiments and analyse the results of recent experiments in this light.Comment: 7 pages, no figure