Driving particle current through narrow channels using classical pump

We study a symmetric exclusion process in which the hopping rates at two chosen adjacent sites vary periodically in time and have a relative phase difference. This mimics a colloidal suspension subjected to external space and time dependent modulation of the diffusion constant. The two special sites act as a classical pump by generating an oscillatory current with a nonzero ${\cal DC}$ value whose direction depends on the applied phase difference. We analyze various features in this model through simulations and obtain an expression for the $\cal{DC}$ current via a novel perturbative treatment.Comment: Revised versio

Percolation Systems away from the Critical Point

This article reviews some effects of disorder in percolation systems even away from the critical density p_c. For densities below p_c, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee-Yang edge singularity problem is described. Rare compact clusters give rise to Griffiths singuraties in the free energy of diluted ferromagnets, and lead to a very slow relaxation of magnetization. In biassed diffusion on percolation clusters, trapping in dead-end branches leads to asymptotic drift velocity becoming zero for strong bias, and very slow relaxation of velocity near the critical bias field.Comment: Minor typos fixed. Submitted to Praman

Thermal and Transport Behavior of Single Crystalline R2CoGa8 (R = Gd, Tb, Dy, Ho, Er, Tm, Lu and Y) Compounds

The anisotropy in electrical transport and thermal behavior of single crystalline R$_{2}$CoGa$_{8}$ series of compounds is presented. These compounds crystallize in a tetragonal structure with space gropup P4/mmm. The nonmagnetic counterparts of the series namely Y$_{2}$CoGa$_{8}$ and Lu$_{2}$CoGa$_{8}$show a behavior consistent with the low density of states at the fermi level. In Y$_{2}$CoGa$_{8}$, a possibility of charge density wave transition is observed at $\approx$ 30 K. Gd$_{2}$CoGa$_{8}$ and Er$_{2}$CoGa$_{8}$ show a presence of short range correlation above the magnetic ordering temperature of the compound. In case of Gd$_{2}$CoGa$_{8}$, the magnetoresistance exhibits a significant anisotropy for current parallel to {[}100{]} and {[}001{]} directions. Compounds with other magnetic rare earths (R = Tb, Dy, Ho and Tm) show the normal expected magnetic behavior whereas Dy$_{2}$CoGa$_{8}$ exhibits the possibility of charge density wave (CDW) transition at approximately same temperature as that of Y$_{2}$CoGa$_{8}$. The thermal property of these compounds is analysed on the basis of crystalline electric field (CEF) calculations.Comment: 10 Pages 14 Figures. Submitted to PR

Heat conduction in the disordered harmonic chain revisited

A general formulation is developed to study heat conduction in disordered harmonic chains with arbitrary heat baths that satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat current J is obtained, from which its asymptotic system-size (N) dependence is extracted. It is shown that the ``thermal conductivity'' depends not just on the system itself but also on the spectral properties of the fluctuation and noise used to model the heat baths. As special cases of our heat baths we recover earlier results which reported that for fixed boundaries $J \sim 1/N^{3/2}$, while for free boundaries $J \sim 1/N^{1/2}$. For other choices we find that one can get other power laws including the ``Fourier behaviour'' $J \sim 1/N$.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Let

Rolling tachyon solution of two-dimensional string theory

We consider a classical (string) field theory of $c=1$ matrix model which was developed earlier in hep-th/9207011 and subsequent papers. This is a noncommutative field theory where the noncommutativity parameter is the string coupling $g_s$. We construct a classical solution of this field theory and show that it describes the complete time history of the recently found rolling tachyon on an unstable D0 brane.Comment: 19 pages, 2 figures, minor changes in text and additional references, correction of decay time (version to appear in JHEP.

From Gravitons to Giants

We discuss exact quantization of gravitational fluctuations in the half-BPS sector around AdS$_5 \times$S$^5$ background, using the dual super Yang-Mills theory. For this purpose we employ the recently developed techniques for exact bosonization of a finite number $N$ of fermions in terms of $N$ bosonic oscillators. An exact computation of the three-point correlation function of gravitons for finite $N$ shows that they become strongly coupled at sufficiently high energies, with an interaction that grows exponentially in $N$. We show that even at such high energies a description of the bulk physics in terms of weakly interacting particles can be constructed. The single particle states providing such a description are created by our bosonic oscillators or equivalently these are the multi-graviton states corresponding to the so-called Schur polynomials. Both represent single giant graviton states in the bulk. Multi-particle states corresponding to multi-giant gravitons are, however, different, since interactions among our bosons vanish identically, while the Schur polynomials are weakly interacting at high enough energies.Comment: v2-references added, minor changes and typos corrected; 24 pages, latex, 3 epsf figure

Correlations and scaling in one-dimensional heat conduction

We examine numerically the full spatio-temporal correlation functions for all hydrodynamic quantities for the random collision model introduced recently. The autocorrelation function of the heat current, through the Kubo formula, gives a thermal conductivity exponent of 1/3 in agreement with the analytical prediction and previous numerical work. Remarkably, this result depends crucially on the choice of boundary conditions: for periodic boundary conditions (as opposed to open boundary conditions with heat baths) the exponent is approximately 1/2. This is expected to be a generic feature of systems with singular transport coefficients. All primitive hydrodynamic quantities scale with the dynamic critical exponent predicted analytically.Comment: 7 pages, 11 figure

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure

Dynamics at a smeared phase transition

We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times.Comment: 10 pages, 8eps figures included, final version as publishe

Solution of a Generalized Stieltjes Problem

We present the exact solution for a set of nonlinear algebraic equations $\frac{1}{z_l}= \pi d + \frac{2 d}{n} \sum_{m \neq l} \frac{1}{z_l-z_m}$. These were encountered by us in a recent study of the low energy spectrum of the Heisenberg ferromagnetic chain \cite{dhar}. These equations are low $d$ (density) ``degenerations'' of more complicated transcendental equation of Bethe's Ansatz for a ferromagnet, but are interesting in themselves. They generalize, through a single parameter, the equations of Stieltjes, $x_l = \sum_{m \neq l} 1/(x_l-x_m)$, familiar from Random Matrix theory. It is shown that the solutions of these set of equations is given by the zeros of generalized associated Laguerre polynomials. These zeros are interesting, since they provide one of the few known cases where the location is along a nontrivial curve in the complex plane that is determined in this work. Using a ``Green's function'' and a saddle point technique we determine the asymptotic distribution of zeros.Comment: 19 pages, 4 figure