Inverse Avalanches On Abelian Sandpiles

A simple and computationally efficient way of finding inverse avalanches for Abelian sandpiles, called the inverse particle addition operator, is presented. In addition, the method is shown to be optimal in the sense that it requires the minimum amount of computation among methods of the same kind. The method is also conceptually nice because avalanche and inverse avalanche are placed in the same footing.Comment: 5 pages with no figure IASSNS-HEP-94/7

Charge and Statistics of Quasiparticles in Fractional Quantum Hall Effec

We have studied here the charge and statistics of quasiparticle excitations in FQH states on the basis of the Berry phase approach incorporating the fact that even number of flux quanta can be gauged away when the Berry phase is removed to the dynamical phase. It is observed that the charge $q$ and statistical parameter $\theta$ of a quasiparticle at filling factor $\nu=\frac{n}{2pn+1}$ are given by $q=(\frac{n}{2pn+1})e$ and $\theta=\frac{n}{2pn+1}$, with the fact that the charge of the quasihole is opposite to that of the quasielectron. Using Laughlin wave function for quasiparticles, numerical studies have been done following the work of Kj{\o}nsberg and Myrheim \cite{KM} for FQH states at $\nu=1/3$ and it is pointed out that as in case of quasiholes, the statistics parameter can be well defined for quasielectrons having the value $\theta=1/3$.Comment: 12 pages, 4 figure

A non-destructive analytic tool for nanostructured materials : Raman and photoluminescence spectroscopy

Modern materials science requires efficient processing and characterization techniques for low dimensional systems. Raman spectroscopy is an important non-destructive tool, which provides enormous information on these materials. This understanding is not only interesting in its own right from a physicist's point of view, but can also be of considerable importance in optoelectronics and device applications of these materials in nanotechnology. The commercial Raman spectrometers are quite expensive. In this article, we have presented a relatively less expensive set-up with home-built collection optics attachment. The details of the instrumentation have been described. Studies on four classes of nanostructures - Ge nanoparticles, porous silicon (nanowire), carbon nanotubes and 2D InGaAs quantum layers, demonstrate that this unit can be of use in teaching and research on nanomaterials.Comment: 32 pages, 13 figure

Generic Sandpile Models Have Directed Percolation Exponents

We study sandpile models with stochastic toppling rules and having sticky grains so that with a non-zero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a small probability of particle loss at each toppling. Generically, for models with a preferred direction, the avalanche exponents are those of critical directed percolation clusters. For undirected models, avalanche exponents are those of directed percolation clusters in one higher dimension.Comment: 4 pages, 4 figures, minor change

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

Quasiquartet CEF ground state with possible quadrupolar ordering in the tetragonal compound YbRu2_{2}Ge2_{2}

e have investigated the magnetic properties of YbRu$_{2}$Ge$_{2}$ by means of magnetic susceptibility $\chi$(T), specific heat C(T) and electrical resistivity $\rho$(T) measurements performed on flux grown single crystals. The Curie-Weiss behavior of $\chi$(T) along the easy plane, the large magnetic entropy at low temperatures and the weak Kondo like increase in $\rho$(T) proves a stable trivalent Yb state. Anomalies in C(T), $\rho$(T) and $\chi$(T) at T$_{0}$ = 10.2 K, T$_{1}$ = 6.5 K and T$_{2}$ = 5.7 K evidence complex ordering phenomena, T$_{0}$ being larger than the highest Yb magnetic ordering temperature found up to now. The magnetic entropy just above T$_{0}$ amounts to almost Rln4, indicating that the crystal electric field (CEF) ground state is a quasiquartet instead of the expected doublet. The behavior at T$_{0}$ is rather unusual and suggest that this transition is related to quadrupolar ordering, being a consequence of the CEF quasiquartet ground state. The combination of a quasiquartet CEF ground state, a high ordering temperature, and the relevance of quadrupolar interactions makes YbRu$_{2}$Ge$_{2}$ a rather unique system among Yb based compounds.Comment: 11 pages, 5 figure, submitted to PRB rapi

Quenched Averages for self-avoiding walks and polygons on deterministic fractals

We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W_n(S), and rooted self-avoiding polygons P_n(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P_n(S), and W_n(S) for an arbitrary point S on the lattice. These are used to compute the averages $, ,$ and $<log W_n(S)>$ over different positions of S. We find that the connectivity constant $\mu$, and the radius of gyration exponent $\nu$ are the same for the annealed and quenched averages. However, $~ n log \mu + (\alpha_q -2) log n$, and $~ n log \mu + (\gamma_q -1)log n$, where the exponents $\alpha_q$ and $\gamma_q$ take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives $\alpha_q \simeq 0.72837 \pm 0.00001$; and $\gamma_q \simeq 1.37501 \pm 0.00003$, to be compared with the annealed values $\alpha_a = 0.73421$ and $\gamma_a = 1.37522$.Comment: 17 pages, 10 figures, submitted to Journal of Statistical Physic

Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the spectral gap, which characterizes the approach to stationarity at large times. We observe boundary induced crossovers in and between massive, diffusive and KPZ scaling regimes.Comment: 4 pages, 2 figures, published versio

Exact Solution of Return Hysteresis Loops in One Dimensional Random Field Ising Model at Zero Temperature

Minor hysteresis loops within the main loop are obtained analytically and exactly in the one-dimensional ferromagnetic random field Ising-model at zero temperature. Numerical simulations of the model show excellent agreement with the analytical results