Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization

Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I superconductors. The hallmark of this model is that the fluctuation spectrum is isotropic and has a minimum at a nonzero wave vector represented by the surface of a d-dimensional hyper-sphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a $\phi ^{4}$ to a $\phi ^{6}$ form with the disordered state metastable for all quench depths. The transition from the disordered to the periodic, lamellar structure changes from second order to first order and suggests that the dynamics is governed by nucleation. Using numerical simulations we have confirmed that the equilibrium free energy function is indeed of a $\phi ^{6}$ form. A study of the dynamics, however, shows that, following a deep quench, the dynamics is described by unstable growth rather than nucleation. A dynamical calculation, based on a generalization of the Brazovskii calculations shows that the disordered state can remain unstable for a long time following the quench.Comment: 18 pages, 15 figures submitted to PR

Efficient method for simulating quantum electron dynamics under the time dependent Kohn-Sham equation

A numerical scheme for solving the time-evolution of wave functions under the time dependent Kohn-Sham equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective Hamiltonian should evolve consistently with each other. For this purpose, a self-consistent loop is required at every time-step for solving the time-evolution numerically, which is computationally expensive. However, in this paper, we develop a different approach expressing a formal solution of the TD-KS equation, and prove that it is possible to solve the TD-KS equation efficiently and accurately by means of a simple numerical scheme without the use of any self-consistent loops.Comment: 5 pages, 3 figures. Physical Review E, 2002, in pres

Static- and dynamical-phase transition in multidimensional voting models on continua

A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle. The reactions of the system are such that two adjacent sites, one empty the other occupied, may evolve to a state where both of these sites are either empty or occupied. The continuum version of this model in a Ddimensional region with boundary is studied, and two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the relaxation of the system toward its stationary state. Based on the first behavior, the static phase transition (discontinuous changes in the stationary profiles of the system) is studied. Based on the second behavior, the dynamical phase transition (discontinuous changes in the relaxation-times of the system) is studied. It is shown that the static phase transition is induced by the bulk reactions only, while the dynamical phase transition is a result of both bulk reactions and boundary conditions.Comment: 10 pages, LaTeX2

Universality and Scaling for the Structure Factor in Dynamic Order-Disorder Transitions

The universal form for the average scattering intensity from systems undergoing order-disorder transitions is found by numerical integration of the Langevin dynamics. The result is nearly identical for simulations involving two different forms of the local contribution to the free energy, supporting the idea that the Model A dynamical universality class includes a wide range of local free-energy forms. An absolute comparison with no adjustable parameters is made to the forms predicted by the theories of Ohta-Jasnow-Kawasaki and Mazenko. The numerical results are well described by the former theory, except in the cross-over region between scattering dominated by domain geometry and scattering determined by Porod's law.Comment: 10 pages incl. 3 figures, Revtex. Submitted to PR

Singular Structure and Enhanced Friedel Oscillations in the Two-Dimensional Electron Gas

We calculate the leading order corrections (in $r_s$) to the static polarization $\Pi^{*}(q,0,)$, with dynamically screened interactions, for the two-dimensional electron gas. The corresponding diagrams all exhibit singular logarithmic behavior in their derivatives at $q=2 k_F$ and provide significant enhancement to the proper polarization particularly at low densities. At a density of $r_s=3$, the contribution from the leading order {\em fluctuational} diagrams exceeds both the zeroth order (Lindhard) response and the self-energy and exchange contributions. We comment on the importance of these diagrams in two-dimensions and make comparisons to an equivalent three-dimensional electron gas; we also consider the impact these finding have on $\Pi^{*}(q,0)$ computed to all orders in perturbation theory

Dynamical properties of the Landau-Ginzburg model with long-range correlated quenched impurities

We investigate the critical dynamics of the time-dependent Landau-Ginzburg model with non conserved n-component order parameter (Model A) in the presence of long-range correlated quenched impurities. We use a special kind of long-range correlations, previously introduced by Weinrib and Halperin. Using a double expansion in \epsilon and \delta we calculate the critical exponent z up to second order on the small parameters. We show that the quenched impurities of this kind affect the critical dynamics already in first order of \epsilon and \delta, leading to a relevant correction for the mean field value of the exponent zComment: 7 pages, REVTEX, to be published in Phys. Rev.

Statics and Dynamics of an Interface in a Temperature Gradient

The response and nonconserved dynamics of a two-phase interface in the presence of a temperature gradient oriented normally to the interface are considered. Two types of boundary conditions on the order parameter are considered, and the structure of the effective free energy and the Langevin equation for the collective coordinate specifying the interface position are analyzed.Comment: 15 pages, Revtex 3.0, 5 figures available upon reques

Structure and vibrational spectra of carbon clusters in SiC

The electronic, structural and vibrational properties of small carbon interstitial and antisite clusters are investigated by ab initio methods in 3C and 4H-SiC. The defects possess sizable dissociation energies and may be formed via condensation of carbon interstitials, e.g. generated in the course of ion implantation. All considered defect complexes possess localized vibrational modes (LVM's) well above the SiC bulk phonon spectrum. In particular, the compact antisite clusters exhibit high-frequency LVM's up to 250meV. The isotope shifts resulting from a_{13}C enrichment are analyzed. In the light of these results, the photoluminescence centers D_{II} and P-U are discussed. The dicarbon antisite is identified as a plausible key ingredient of the D_{II}-center, whereas the carbon split-interstitial is a likely origin of the P-T centers. The comparison of the calculated and observed high-frequency modes suggests that the U-center is also a carbon-antisite based defect.Comment: 15 pages, 6 figures, accepted by Phys. Rev.

Infrared Behavior of Interacting Bosons at Zero Temperature

We exploit the symmetries associated with the stability of the superfluid phase to solve the long-standing problem of interacting bosons in the presence of a condensate at zero temperature. Implementation of these symmetries poses strong conditions on the renormalizations that heal the singularities of perturbation theory. The renormalized theory gives: For d>3 the Bogoliubov quasiparticles as an exact result; for 1<d<=3 a nontrivial solution with the exact exponent for the singular longitudinal correlation function, with phonons again as low-lying excitations.Comment: Minor Changes. 4 pages, RevTeX, no figures, uses multicol.sty e-mail: [email protected]

Scaling of thermal conductivity of helium confined in pores

We have studied the thermal conductivity of confined superfluids on a bar-like geometry. We use the planar magnet lattice model on a lattice $H\times H\times L$ with $L \gg H$. We have applied open boundary conditions on the bar sides (the confined directions of length $H$) and periodic along the long direction. We have adopted a hybrid Monte Carlo algorithm to efficiently deal with the critical slowing down and in order to solve the dynamical equations of motion we use a discretization technique which introduces errors only $O((\delta t)^6)$ in the time step $\delta t$. Our results demonstrate the validity of scaling using known values of the critical exponents and we obtained the scaling function of the thermal resistivity. We find that our results for the thermal resistivity scaling function are in very good agreement with the available experimental results for pores using the tempComment: 5 two-column pages, 3 figures, Revtex