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arXiv2003

Quasi-classical Approach to Bose Condensation in a Finite Potential Well

We treat the problem of self-consistently interacting bosons in the presence of a finite (but macroscopic) potential well within a quasi-classical approximation for the normal component and the order parameter. We solve the equilibrium problem and show, that actually condensation occurs in two steps. One already at low densities with Bose condensation only in the well and another one corresponding to the usual condensation in bulk. The peak and width of the distribution of trapped particles in the well display a distinct signature of the local condensation. A possible connection to recent experiments with excitons is discussed.

cond-mat↗

arXiv2003

Berry's Phases of Ground States of Interacting Spin-One Bosons: Chains of Monopoles and Monosegments

We study Berry's connection potentials of many-body ground states of spin-one bosons with antiferromagnetic interactions in adiabatically varying magnetic fields. We find that Berry's connection potentials are generally determined by, instead of usual singular monopoles, linearly positioned monosegments each of which carries one unit of topological charge; in the absence of a magnetic field gradient this distribution of monosegments becomes a linear chain of monopoles. Consequently, Berry's phases consist of a series of step functions of magnetic fields; a magnetic field gradient causes rounding of these step-functions. We also calculate Berry's connection fields, profiles of monosegments and show that the total topological charge is conserved in a parameter space.

cond-mat↗

arXiv1994

The Phases and Triviality of Scalar Quantum Electrodynamics

The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs'') field and treats the gauge field as non-compact. The phase diagram is two dimensional. No fine tuning or extrapolations are needed to study the theory's critical behovior. Two lines of second order phase transitions are discovered and the scaling laws for each are studied by finite size scaling methods on lattices ranging from $6^4$ through $24^4$. One line corresponds to monopole percolation and the other to a transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent specific heats. The lines of transitions cross in the interior of the phase diagram and appear to be unrelated. The monopole percolation transition has critical indices which are compatible with ordinary four dimensional percolation uneffected by interactions. Finite size scaling and histogram methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line are well-fit by the hypothesis that scalar quantum electrodynamics is logarithmically trivial. The logarithms are measured in both finite size scaling of the specific heat peaks as a function of volume as well as in the coupling constant dependence of the specific heats measured on fixed but large lattices. The theory is seen to be qualitatively similar to $λϕ^{4}$. The standard CRAY random number generator RANF proved to be inadequate

hep-lat↗

arXiv1998

Boundary fields and renormalization group flow in the two-matrix model

We analyze the Ising model on a random surface with a boundary magnetic field using matrix model techniques. We are able to exactly calculate the disk amplitude, boundary magnetization and bulk magnetization in the presence of a boundary field. The results of these calculations can be interpreted in terms of renormalization group flow induced by the boundary operator. In the continuum limit this RG flow corresponds to the flow from non-conformal to conformal boundary conditions which has recently been studied in flat space theories.

hep-th↗

arXiv1995

Polymer-Chain Adsorption Transition at a Cylindrical Boundary

In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in $D$ dimensions to an anisotropic one-dimensional random walk on concentric hyperspheres. Here, I construct such a random walk to model the adsorption-desorption transition of polymer chains growing near an attractive cylindrical boundary such as that of a cell membrane. I find that the fraction of adsorbed monomers on the boundary vanishes exponentially when the adsorption energy decreases towards its critical value. When the adsorption energy rises beyond a certain value above the critical point whose scale is set by the radius of the cell, the adsorption fraction exhibits a crossover to a linear increase characteristic to polymers growing near planar boundaries.

hep-lat↗

arXiv1995

Kinetics of A+B--->0 with Driven Diffusive Motion

We study the kinetics of two-species annihilation, A+B--->0, when all particles undergo strictly biased motion in the same direction and with an excluded volume repulsion between same species particles. It was recently shown that the density in this system decays as t^{-1/3}, compared to t^{-1/4} density decay in A+B--->0 with isotropic diffusion and either with or without the hard-core repulsion. We suggest a relatively simple explanation for this t^{-1/3} decay based on the Burgers equation. Related properties associated with the asymptotic distribution of reactants can also be accounted for within this Burgers equation description.

cond-mat↗

arXiv1995

Correlations in Ising chains with non-integrable interactions

Two-spin correlations generated by interactions which decay with distance r as r^{-1-sigma} with -1 \infty, but they contain a singular structure for r/L -> 0 which can be observed by introducing magnified correlations, LC(r,L)-\sum_r C(r,L). The magnified correlations are shown to have a scaling form F(r/L) and the singular structure of F(x) for x->0 is found to be the same at all temperatures including the critical point. These conclusions are supported by the results of Monte Carlo simulations for systems with sigma =-0.50 and -0.25 both at the critical temperature T=Tc and at T=2Tc.

cond-mat↗

arXiv1995

Pinning of a solid--liquid--vapour interface by stripes of obstacles

We use a macroscopic Hamiltonian approach to study the pinning of a solid--liquid--vapour contact line on an array of equidistant stripes of obstacles perpendicular to the liquid. We propose an estimate of the density of pinning stripes for which collective pinning of the contact line happens. This estimate is shown to be in good agreement with Langevin equation simulation of the macroscopic Hamiltonian. Finally we introduce a 2--dimensional mean field theory which for small strength of the pinning stripes and for small capillary length gives an excellent description of the averaged height of the contact line.

cond-mat↗

arXiv1995

Method for Generating Long-Range Correlations for Large Systems

We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We apply the algorithm to generate enhanced diffusion, isotropic and anisotropic self-affine surfaces, and isotropic and anisotropic correlated percolation.

cond-mat↗

arXiv1996

Equation of State of the Hard-Sphere Crystal

A new approach to the averaged two-particle distribution function of a crystalline phase is presented. It includes an indirect check of the merit of the Gaussian approximation for the local density and a new way to inferring values of the thermodynamic variables from simulation data. The equation of state and the compressibility of the hard-sphere FCC crystal is computed from Tarazona free energy density functional [Phys. Rev. A {\bf 31}, 2672 (1985)]. They are in excellent agreement with simulation results over the physical range of densities up to almost close packing. We also include the comparison with the results obtained by two other functional approaches which are also excellent.

cond-mat↗

arXiv1996

Anomalous density dependence of static friction in sand

We measured experimentally the static friction force $F_s$ on the surface of a glass rod immersed in dry sand. We observed that $F_s$ is extremely sensitive to the closeness of packing of grains. A linear increase of the grain-density yields to an exponentially increasing friction force. We also report on a novel periodicity of $F_s$ during gradual pulling out of the rod. Our observations demonstrate the central role of grain bridges and arches in the macroscopic properties of granular packings.

cond-mat↗

arXiv1996

Synchronization of Integrate and Fire oscillators with global coupling

In this article we study the behavior of globally coupled assemblies of a large number of Integrate and Fire oscillators with excitatory pulse-like interactions. On some simple models we show that the additive effects of pulses on the state of Integrate and Fire oscillators are sufficient for the synchronization of the relaxations of all the oscillators. This synchronization occurs in two forms depending on the system: either the oscillators evolve ``en bloc'' at the same phase and therefore relax together or the oscillators do not remain in phase but their relaxations occur always in stable avalanches. We prove that synchronization can occur independently of the convexity or concavity of the oscillators evolution function. Furthermore the presence of disorder, up to some level, is not only compatible with synchronization, but removes some possible degeneracy of identical systems and allows new mechanisms towards this state.

cond-mat↗

arXiv1996

Self-organized branching processes: Avalanche models with dissipation

We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the model self-organizes not into a critical state but rather into a subcritical state: when dissipation is present, the dynamical fixed point does not coincide with the critical point. Thus the level of dissipation acts as a relevant parameter in the renormalization-group sense. We study the model numerically and compute analytically the critical exponents for the avalanche size and lifetime distributions and the scaling exponents for the corresponding cutoffs.

cond-mat↗

arXiv1996

Anomalous Scaling in the N-Point Functions of Passive Scalar

A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the 2-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed.

chao-dyn↗

arXiv1996

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $ξ\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=ρ(r) t^{-1/2} ξ^{-2} f_d(ξ)$, where $ρ(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(ξ)$ in powers of $ξ$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(ξ)$. Namely, for $d=2$, $f_2(ξ)\simeq a_2ξ^2\lnξ+b_2ξ^2$; for $3\le d\le 5$, $f_d(ξ)\simeq a_dξ^2+b_dξ^d$; for $d=6$, $f_6(ξ)\simeq a_6ξ^2+b_6ξ^6\lnξ$; for $7\le d\le 9$, $f_d(ξ)\simeq a_dξ^2+b_dξ^6+c_dξ^d$; for $d=10$, $f_{10}(ξ)\simeq a_{10}ξ^2+b_{10}ξ^6+c_{10}ξ^{10}\lnξ$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/ρ(r)\simeq t^{-1/2}\ln t$.

cond-mat↗

arXiv1996

Crossover from directed percolation to compact directed percolation

We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical exponents switch from the compact directed percolation class to ordinary directed percolation. We conclude that the nonuniversality observed in models with multiple absorbing configurations cannot be explained as a simple surface effect.

cond-mat↗

arXiv1996

Thermodynamics of Coupled Identical Oscillators within the Path Integral Formalism

A generalization of symmetrized density matrices in combination with the technique of generating functions allows to calculate the partition function of identical particles in a parabolic confining well. Harmonic two-body interactions (repulsive or attractive) are taken into account. Also the influence of a homogeneous magnetic field, introducing anisotropy in the model, is examined. Although the theory is developed for fermions and bosons, special attention is payed to the thermodynamic properties of bosons and their condensation.

cond-mat↗

arXiv1996

On the VC-dimension of neural networks with binary weights

We investigate the VC-dimension of the perceptron and simple two-layer networks like the committee- and the parity-machine with weights restricted to values $\pm1$. For binary inputs, the VC-dimension is determined by atypical pattern sets, i.e. it cannot be found by replica analysis or numerical Monte Carlo sampling. For small systems, exhaustive enumerations yield exact results. For systems that are too large for enumerations, number theoretic arguments give lower bounds for the VC-dimension. For the Ising perceptron, the VC-dimension is probably larger than $N/2$.

cond-mat↗