Bloch Walls and Macroscopic String States in Bethe's solution of the Heisenberg Ferromagnetic Linear Chain

We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1-d for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. These are identified as generalized quantum Bloch wall states, and a simple physical picture provided for the same.Comment: 4 pages, RevTex, 2 figures, Submitted to Phys. Rev. Let

Effect of Noise on Patterns Formed by Growing Sandpiles

We consider patterns generated by adding large number of sand grains at a single site in an abelian sandpile model with a periodic initial configuration, and relaxing. The patterns show proportionate growth. We study the robustness of these patterns against different types of noise, \textit{viz.}, randomness in the point of addition, disorder in the initial periodic configuration, and disorder in the connectivity of the underlying lattice. We find that the patterns show a varying degree of robustness to addition of a small amount of noise in each case. However, introducing stochasticity in the toppling rules seems to destroy the asymptotic patterns completely, even for a weak noise. We also discuss a variational formulation of the pattern selection problem in growing abelian sandpiles.Comment: 15 pages,16 figure

Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice

We study the quasiadiabatic dynamics of a one-dimensional system of ultracold bosonic atoms loaded in an optical superlattice. Focusing on a slow linear variation in time of the superlattice potential, the system is driven from a conventional Mott insulator phase to a superlattice-induced Mott insulator, crossing in between a gapless critical superfluid region. Due to the presence of a gapless region, a number of defects depending on the velocity of the quench appear. Our findings suggest a power-law dependence similar to the Kibble-Zurek mechanism for intermediate values of the quench rate. For the temporal ranges of the quench dynamics that we considered, the scaling of defects depends nontrivially on the width of the superfluid region.Comment: 6 Pages, 4 Figure

Eulerian Walkers as a model of Self-Organised Criticality

We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On closed graphs these walks generate Euler circuits. On open graphs, the particle eventually leaves the system, and a new particle is then added. The operators corresponding to particle addition generate an abelian group, same as the group for the Abelian Sandpile model on the graph. We determine the critical steady state and some critical exponents exactly, using this equivalence.Comment: 4 pages, RevTex, 4 figure

One step growth of GaN/SiO2 core/shell nanowire in vapor-liquid-solid route by chemical vapor deposition technique

GaN/SiO2 core/shell nanowires are grown by cobalt phthalocyanine catalyst assisted vapor-liquid-solid route, in which Si wafer coated with a mixture of gallium and indium is used as the source for Ga and Si and ammonia is used as the precursor for nitrogen and hydrogen. Gallium in the presence of indium and hydrogen, which results from the dissociation of ammonia, forms Si-Ga-In alloy at the growth temperature around 910 degree Celsius. This alloy acts as the source of Si, Ga and In. A detailed study using a variety of characterization tools reveals that these wires, which are several tens of micron long, has a diameter distribution of the core ranging from 20 to 50 nm, while the thickness of the amorphous SiO2 shell layer is about 10 nm. These wires grow along direction. It has also been observed that the average width of these wires decreases, while their density increases as the gallium proportion in the Ga-In mixture is increased.Comment: 14 pages, 4 figure

Nonequilibrium Phase Transitions in a Driven Sandpile Model

We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope \sigma_c\/, a parameter \alpha\/, governing the local current-slope relation (beyond threshold), and $j_{\rm in}$, the mean input current of sand. A nonequilibrium phase diagram is obtained in the \alpha\, -\, j_{\rm in}\/ plane. We find an infinity of phases, characterized by different mean slopes and separated by continuous or first-order boundaries, some of which we obtain analytically. Extensions to two dimensions are discussed.Comment: 11 pages, RevTeX (preprint format), 4 figures available upon requs

The Irreducible String and an Infinity of Additional Constants of Motion in a Deposition-Evaporation Model on a Line

We study a model of stochastic deposition-evaporation with recombination, of three species of dimers on a line. This model is a generalization of the model recently introduced by Barma {\it et. al.} (1993 {\it Phys. Rev. Lett.} {\bf 70} 1033) to $q\ge 3$ states per site. It has an infinite number of constants of motion, in addition to the infinity of conservation laws of the original model which are encoded as the conservation of the irreducible string. We determine the number of dynamically disconnected sectors and their sizes in this model exactly. Using the additional symmetry we construct a class of exact eigenvectors of the stochastic matrix. The autocorrelation function decays with different powers of $t$ in different sectors. We find that the spatial correlation function has an algebraic decay with exponent 3/2, in the sector corresponding to the initial state in which all sites are in the same state. The dynamical exponent is nontrivial in this sector, and we estimate it numerically by exact diagonalization of the stochastic matrix for small sizes. We find that in this case $z=2.39\pm0.05$.Comment: Some minor errors in the first version has been correcte

Numerical Diagonalisation Study of the Trimer Deposition-Evaporation Model in One Dimension

We study the model of deposition-evaporation of trimers on a line recently introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain with three-spin couplings given by H= \sum\displaylimits_i [(1 - \sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+ + h.c]. We study by exact numerical diagonalization of $H$ the variation of the gap in the eigenvalue spectrum with the system size for rings of size up to 30. For the sector corresponding to the initial condition in which all sites are empty, we find that the gap vanishes as $L^{-z}$ where the gap exponent $z$ is approximately $2.55\pm 0.15$. This model is equivalent to an interfacial roughening model where the dynamical variables at each site are matrices. From our estimate for the gap exponent we conclude that the model belongs to a new universality class, distinct from that studied by Kardar, Parisi and Zhang.Comment: 11 pages, 2 figures (included