A nested sequence of projectors and corresponding braid matrices R^(θ)\hat R(\theta): (1) Odd dimensions

A basis of $N^2$ projectors, each an ${N^2}\times{N^2}$ matrix with constant elements, is implemented to construct a class of braid matrices $\hat{R}(\theta)$, $\theta$ being the spectral parameter. Only odd values of $N$ are considered here. Our ansatz for the projectors $P_{\alpha}$ appearing in the spectral decomposition of $\hat{R}(\theta)$ leads to exponentials $exp(m_{\alpha}\theta)$ as the coefficient of $P_{\alpha}$. The sums and differences of such exponentials on the diagonal and the antidiagonal respectively provide the $(2N^2 -1)$ nonzero elements of $\hat{R}(\theta)$. One element at the center is normalized to unity. A class of supplementary constraints imposed by the braid equation leaves ${1/2}(N+3)(N-1)$ free parameters $m_{\alpha}$. The diagonalizer of $\hat{R}(\theta)$ is presented for all $N$. Transfer matrices $t(\theta)$ and $L(\theta)$ operators corresponding to our $\hat{R}(\theta)$ are studied. Our diagonalizer signals specific combinations of the components of the operators that lead to a quadratic algebra of $N^2$ constant $N\times N$ matrices. The $\theta$-dependence factors out for such combinations. $\hat R(\theta)$ is developed in a power series in $\theta$. The basic difference arising for even dimensions is made explicit. Some special features of our $\hat{R}(\theta)$ are discussed in a concluding section.Comment: latex file, 32 page

Fluctuation Cumulant Behavior for the Field-Pulse Induced Magnetisation-Reversal Transition in Ising Models

The universality class of the dynamic magnetisation-reversal transition, induced by a competing field pulse, in an Ising model on a square lattice, below its static ordering temperature, is studied here using Monte Carlo simulations. Fourth order cumulant of the order parameter distribution is studied for different system sizes around the phase boundary region. The crossing point of the cumulant (for different system sizes) gives the transition point and the value of the cumulant at the transition point indicates the universality class of the transition. The cumulant value at the crossing point for low temperature and pulse width range is observed to be significantly less than that for the static transition in the same two-dimensional Ising model. The finite size scaling behaviour in this range also indicates a higher correlation length exponent value. For higher temperature and pulse width range, the transition seems to fall in a mean-field like universality class.Comment: 5 pages, 8 eps figures, thoroughly revised manuscript with new figures, accepted in Phys. Rev. E (2003

The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra

Using a contraction procedure, we construct a twist operator that satisfies a shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra. The corresponding universal ${\cal R}_{h}(y)$ matrix obeys a Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a class of representations, the dynamical Yang-Baxter equation may be expressed as a compatibility condition for the algebra of the Lax operators.Comment: Latex, 9 pages, no figure

Length and time scale divergences at the magnetization-reversal transition in the Ising model

The divergences of both the length and time scales, at the magnetization- reversal transition in Ising model under a pulsed field, have been studied in the linearized limit of the mean field theory. Both length and time scales are shown to diverge at the transition point and it has been checked that the nature of the time scale divergence agrees well with the result obtained from the numerical solution of the mean field equation of motion. Similar growths in length and time scales are also observed, as one approaches the transition point, using Monte Carlo simulations. However, these are not of the same nature as the mean field case. Nucleation theory provides a qualitative argument which explains the nature of the time scale growth. To study the nature of growth of the characteristic length scale, we have looked at the cluster size distribution of the reversed spin domains and defined a pseudo-correlation length which has been observed to grow at the phase boundary of the transition.Comment: 9 pages Latex, 3 postscript figure

Particle Acceleration in Advection-Dominated Accretion Disks with Shocks: Green's Function Energy Distribution

The distribution function describing the acceleration of relativistic particles in an advection-dominated accretion disk is analyzed using a transport formalism that includes first-order Fermi acceleration, advection, spatial diffusion, and the escape of particles through the upper and lower surfaces of the disk. When a centrifugally-supported shock is present in the disk, the concentrated particle acceleration occurring in the vicinity of the shock channels a significant fraction of the binding energy of the accreting gas into a population of relativistic particles. These high-energy particles diffuse vertically through the disk and escape, carrying away both energy and entropy and allowing the remaining gas to accrete. The dynamical structure of the disk/shock system is computed self-consistently using a model previously developed by the authors that successfully accounts for the production of the observed relativistic outflows (jets) in M87 and \SgrA. This ensures that the rate at which energy is carried away from the disk by the escaping relativistic particles is equal to the drop in the radial energy flux at the shock location, as required for energy conservation. We investigate the influence of advection, diffusion, and acceleration on the particle distribution by computing the nonthermal Green's function, which displays a relatively flat power-law tail at high energies. We also obtain the energy distribution for the particles escaping from the disk, and we conclude by discussing the spectrum of the observable secondary radiation produced by the escaping particles.Comment: Published in Ap

Satellite observations of thought experiments close to a black hole

Since black holes are `black', methods of their identification must necessarily be indirect. Due to very special boundary condition on the horizon, the advective flow behaves in a particular way, which includes formation of centrifugal pressure dominated boundary layer or CENBOL where much of the infall energy is released and outflows are generated. The observational aspects of black holes must depend on the steady and time-dependent properties of this boundary layer. Several observational results are written down in this review which seem to support the predictions of thought experiments based on this advective accretion/outflow model. In future, when gravitational waves are detected, some other predictions of this model could be tested as well.Comment: Published in Classical and Quantum Gravity, v. 17, No. 12, p. 2427, 200

Generalized boson algebra and its entangled bipartite coherent states

Starting with a given generalized boson algebra U_(h(1)) known as the bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ the Hopf duality arguments to provide the dually conjugate function algebra Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a closed form expression of the universal T matrix that caps the duality and generalizes the familiar exponential map relating a Lie algebra with its corresponding group. Subsequently, using an inverse Mellin transform approach, the coherent states of single-node systems subject to the U_(h(1)) symmetry are found to be complete with a positive-definite integration measure. Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur

Properties of non-BPS SU(3) monopoles

This paper is concerned with magnetic monopole solutions of SU(3) Yang-Mills-Higgs system beyond the Bogomol'nyi-Prasad-Sommerfield limit. The different SU(2) embeddings, which correspond to the fundamental monopoles, as well the embedding along composite root are studied. The interaction of two different fundamental monopoles is considered. Dissolution of a single fundamental non-BPS SU(3) monopole in the limit of the minimal symmetry breaking is analysed.Comment: 19 pages, 7 figures. Typos corrected, reference added. Final version published in Physica Script