Three-Body Recombination in One Dimension

We study the three-body problem in one dimension for both zero and finite range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all combinations of the parity and exchange symmetries. For bosons, we provide a numerical demonstration of several universal features that appear in the three-body system, and discuss how certain universal features in three dimensions are different in one dimension. We show that the probability for inelastic processes vanishes as the range of the pair-wise interaction is taken to zero and demonstrate numerically that the recombination threshold law manifests itself for large scattering length.Comment: 15 pages 7 figures Submitted to Physical Review

Universality in Complex Networks: Random Matrix Analysis

We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow universal Gaussian orthogonal ensemble statistics of random matrix theory. Secondly we show an analogy between the onset of small-world behavior, quantified by the structural properties of networks, and the transition from Poisson to Gaussian orthogonal ensemble statistics, quantified by Brody parameter characterizing a spectral property. We also present our analysis for a protein-protein interaction network in budding yeast.Comment: 4+ pages, 4 figures, to appear in PRE, major change in the paper including titl

Computational Investigation of Furnace Wall for Silica Ramming Mass with FDM

Furnaces are useful for melting different materials for casting process. In this research paper, we had done advanced heat transfer analysis of induction furnace wall made of silica ramming mass using explicit finite difference method. We have divided actual geometry of furnace refractory wall into 14 elements and 24 nodes. We have derived explicit finite difference equations for all 24 nodes. We have calculated temperature distribution and thermal stress distribution for all different nodes with respect to time. We have plotted graphs for maximum temperature v/s time and maximum stress v/s time. We found that results indicate the effect of thermal fatigue in the induction furnace wall for silica ramming mass. The analysis is very helpful in understanding how thermal fatigue failure of refractory wall happens

Numerical study of spin quantum Hall transitions in superconductors with broken time-reversal symmetry

We present results of numerical studies of spin quantum Hall transitions in disordered superconductors, in which the pairing order parameter breaks time-reversal symmetry. We focus mainly on p-wave superconductors in which one of the spin components is conserved. The transport properties of the system are studied by numerically diagonalizing pairing Hamiltonians on a lattice, and by calculating the Chern and Thouless numbers of the quasiparticle states. We find that in the presence of disorder, (spin-)current carrying states exist only at discrete critical energies in the thermodynamic limit, and the spin-quantum Hall transition driven by an external Zeeman field has the same critical behavior as the usual integer quantum Hall transition of non-interacting electrons. These critical energies merge and disappear as disorder strength increases, in a manner similar to those in lattice models for integer quantum Hall transition.Comment: 9 pages, 9 figure

A simple topological model with continuous phase transition

In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e. invariant under reflection of coordinates) have been found out. In this paper we present a simple topological model satisfying the above conditions hoping to enlighten the mechanism which causes this phenomenon in more general physical models. The symmetry breaking is testified by a continuous magnetization with a nonanalytic point in correspondence of a critical temperature which divides the broken symmetry phase from the unbroken one. A particularity with respect to the common pictures of a phase transition is that the nonanalyticity of the magnetization is not accompanied by a nonanalytic behavior of the free energy.Comment: 17 pages, 7 figure

Multi-Channel Transport in Disordered Medium under Generic Scattering Conditions

Our study of the evolution of transmission eigenvalues, due to changes in various physical parameters in a disordered region of arbitrary dimensions, results in a generalization of the celebrated DMPK equation. The evolution is shown to be governed by a single complexity parameter which implies a deep level of universality of transport phenomena through a wide range of disordered regions. We also find that the interaction among eigenvalues is of many body type that has important consequences for the statistical behavior of transport properties.Comment: 19 Pages, No Figure

Mn(II), Fe(II), Co(II), Ni(II), Cu(II), Zn(II), Pd(II), Cd(II) & UO2(II) Chelates of Schiff Bases Derived from o-Aminobenzenesulphonic Acid & 2-Aminoethanesulphonic Acid & 2-Hydroxy-1-naphthaldehyde

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Heat transport of clean spin-ladders coupled to phonons: Umklapp scattering and drag

We study the low-temperature heat transport in clean two-leg spin ladder compounds coupled to three-dimensional phonons. We argue that the very large heat conductivities observed in such systems can be traced back to the existence of approximate symmetries and corresponding weakly violated conservation laws of the effective (gapful) low--energy model, namely pseudo-momenta. Depending on the ratios of spin gaps and Debye energy and on the temperature, the magnetic contribution to the heat conductivity can be positive or negative, and exhibit an activated or anti-activated behavior. In most regimes, the magnetic heat conductivity is dominated by the spin-phonon drag: the excitations of the two subsystems have almost the same drift velocity, and this allows for an estimate of the ratio of the magnetic and phononic contributions to the heat conductivity.Comment: revised version, 8 pages, 3 figures, added appendi