Transport Properties of Solitons

We calculate in this article the transport coefficients which characterize the dynamics of solitons in quantum field theory using the methods of dissipative quantum systems. We show how the damping and diffusion coefficients of soliton-like excitations can be calculated using the integral functional formalism. The model obtained in this article has new features which cannot be obtained in the standard models of dissipation in quantum mechanics.Comment: 16 Pages, RevTeX, Preprint UIU

Diffusion limited aggregation as a Markovian process. Part I: bond-sticking conditions

Cylindrical lattice Diffusion Limited Aggregation (DLA), with a narrow width N, is solved using a Markovian matrix method. This matrix contains the probabilities that the front moves from one configuration to another at each growth step, calculated exactly by solving the Laplace equation and using the proper normalization. The method is applied for a series of approximations, which include only a finite number of rows near the front. The matrix is then used to find the weights of the steady state growing configurations and the rate of approaching this steady state stage. The former are then used to find the average upward growth probability, the average steady-state density and the fractal dimensionality of the aggregate, which is extrapolated to a value near 1.64.Comment: 24 pages, 20 figure

Scaling exponent of the maximum growth probability in diffusion-limited aggregation

An early (and influential) scaling relation in the multifractal theory of Diffusion Limited Aggregation(DLA) is the Turkevich-Scher conjecture that relates the exponent \alpha_{min} that characterizes the ``hottest'' region of the harmonic measure and the fractal dimension D of the cluster, i.e. D=1+\alpha_{min}. Due to lack of accurate direct measurements of both D and \alpha_{min} this conjecture could never be put to serious test. Using the method of iterated conformal maps D was recently determined as D=1.713+-0.003. In this Letter we determine \alpha_{min} accurately, with the result \alpha_{min}=0.665+-0.004. We thus conclude that the Turkevich-Scher conjecture is incorrect for DLA.Comment: 4 pages, 5 figure

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Time evolution of damage under variable ranges of load transfer

We study the time evolution of damage in a fiber bundle model in which the range of interaction of fibers varies through an adjustable stress transfer function recently introduced. We find that the lifetime of the material exhibits a crossover from mean field to short range behavior as in the static case. Numerical calculations showed that the value at which the transition takes place depends on the system's disorder. Finally, we have performed a microscopic analysis of the failure process. Our results confirm that the growth dynamics of the largest crack is radically different in the two limiting regimes of load transfer during the first stages of breaking.Comment: 8 pages, 7 figures, revtex4 styl

Boson gas in a periodic array of tubes

We report the thermodynamic properties of an ideal boson gas confined in an infinite periodic array of channels modeled by two, mutually perpendicular, Kronig-Penney delta-potentials. The particle's motion is hindered in the x-y directions, allowing tunneling of particles through the walls, while no confinement along the z direction is considered. It is shown that there exists a finite Bose- Einstein condensation (BEC) critical temperature Tc that decreases monotonically from the 3D ideal boson gas (IBG) value $T_{0}$ as the strength of confinement $P_{0}$ is increased while keeping the channel's cross section, $a_{x}a_{y}$ constant. In contrast, Tc is a non-monotonic function of the cross-section area for fixed $P_{0}$. In addition to the BEC cusp, the specific heat exhibits a set of maxima and minima. The minimum located at the highest temperature is a clear signal of the confinement effect which occurs when the boson wavelength is twice the cross-section side size. This confinement is amplified when the wall strength is increased until a dimensional crossover from 3D to 1D is produced. Some of these features in the specific heat obtained from this simple model can be related, qualitatively, to at least two different experimental situations: $^4$He adsorbed within the interstitial channels of a bundle of carbon nanotubes and superconductor-multistrand-wires Nb$_{3}$Sn.Comment: 9 pages, 10 figures, submitte

Berry phases and pairing symmetry in Holstein-Hubbard polaron systems

We study the tunneling dynamics of dopant-induced hole polarons which are self-localized by electron-phonon coupling in a two-dimensional antiferro- magnet. Our treatment is based on a path integral formulation of the adia- batic approximation, combined with many-body tight-binding, instanton, con- strained lattice dynamics, and many-body exact diagonalization techniques. Our results are mainly based on the Holstein-$tJ$ and, for comparison, on the Holstein-Hubbard model. We also study effects of 2nd neighbor hopping and long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics is mapped onto an effective low-energy Hamiltonian which takes the form of a fermion tight-binding model with occupancy dependent, predominant- ly 2nd and 3rd neighbor tunneling matrix elements, excluded double occupan- cy, and an effective intersite charge interactions. Antiferromagnetic spin correlations in the original many-electron Hamiltonian are reflected by an attractive contribution to the 1st neighbor charge interaction and by Berry phase factors which determine the signs of effective polaron tunneling ma- trix elements. In the two-polaron case, these phase factors lead to polaron pair wave functions of either $d_{x^2-y^2}$-wave symmetry or p-wave symme- try with zero and nonzero total pair momentum, respectively. Implications for the doping dependent isotope effect, pseudo-gap and Tc of a superconduc- ting polaron pair condensate are discussed/compared to observed in cuprates.Comment: 23 pages, revtex, 13 ps figure

Cylindrical microemulsions: a polymer-like phase ?

The regions of stability of spherical, cylindrical, and lamellar phases of microemulsions are calculated within mean-field theory. In the cylindrical phase, thermal fluctuations determine a temperature dependent persistence length below which the cylinders are rigid (rod-like) and above which the cylinders are flexible (polymer-like). The length of the polymer-like chains depends on concentration and temperature. The radii of gyration of these flexible microemulsions are also calculated.Nous calculons les zones de stabilité des phases de microémulsions sphériques, cylindriques et lamellaires en théorie de champ moyen. Dans la phase cylindrique, les fluctuations thermiques déterminent une longueur de persistance dépendant de la température. A une échelle inférieure à cette longueur les cylindres sont rigides (bâtonnets), tandis qu'à plus grande échelle, les cylindres sont flexibles (comme des polymères). La longueur de ces cylindres flexibles dépend de la concentration et de la température. Nous calculons également leur rayon de giration

Conformations of polydisperse polymer solutions : bimodal distribution

Starting with the Flory theory for one long flexible polymer chain of N segments in a homopolymer melt of shorter (P segments) chains, we employ scaling arguments to construct the « phase diagram » of an athermal bimodal solution, i.e. a ternary system composed of N chains, P chains, and solvent. Qualitatively the presence of short chains reduces the effective solvent quality as experienced by the long chains. We present limiting forms for the radii of gyration of both chains through out the « phase diagram ».Partant de la théorie de Flory pour une chaîne linéaire flexible de N monomères dans un polymère fondu de chaînes plus courtes (P monomères) on emploie des arguments d'échelle pour établir le « diagramme de phase » d'une solution bimodale athermique (système ternaire composé de chaînes N, de chaînes P et d'un solvant). Qualitativement la présence des chaînes courtes peut s'interpréter comme une réduction de la qualité du solvant effectif qui entoure les longues chaînes. On indique des lois asymptotiques pour le rayon de giration dans les différentes régions de ce diagramme de phase