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

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

Effect of realistic interatomic interactions and two-body correlation on the heat capacity of a trapped BEC

An approximate many-body theory has been used to calculate the heat capacity and the condensate fraction of a BEC with effective repulsive interaction. The effect of interactions has been analyzed and compared with the non-interacting case. It has been found that the repulsive interaction lowers the critical temperature from the value found in the non-interacting case. The difference between the critical temperatures increases with the increase in the total number of atoms in the trap.Comment: 15 pages, 5 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

On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice

A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended states in this system, for which only numerical evidence is available in the literature so far. The present work also sheds light on the restrictive conditions under which the extended states are supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in Physical Review Letter

Boltzmann-Shannon Entropy: Generalization and Application

The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some new interesting results of significant physical importance.Comment: 5 pages, Accepted in Mod.Phys.Lett.

Mass Outflow Rate From Accretion Discs around Compact Objects

We compute mass outflow rates from accretion disks around compact objects, such as neutron stars and black holes. These computations are done using combinations of exact transonic inflow and outflow solutions which may or may not form standing shock waves. Assuming that the bulk of the outflow is from the effective boundary layers of these objects, we find that the ratio of the outflow rate and inflow rate varies anywhere from a few percent to even close to a hundred percent (i.e., close to disk evacuation case) depending on the initial parameters of the disk, the degree of compression of matter near the centrifugal barrier, and the polytropic index of the flow. Our result, in general, matches with the outflow rates obtained through a fully time-dependent numerical simulation. In some region of the parameter space when the standing shock does not form, our results indicate that the disk may be evacuated and may produce quiescence states.Comment: 30 Latex pages and 13 figures. crckapb.sty; Published in Class. Quantum Grav. Vol. 16. No. 12. Pg. 387

Phases, many-body entropy measures and coherence of interacting bosons in optical lattices

Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator and fermionized Tonks gases can be probed in such systems. To detect these phases -- pivotal for both experiment and theory -- as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground-state for lattices with commensurate filling (i.e. an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schr\"odinger equation. We demonstrate that all emergent phases -- the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by our many-body entropy measures and by Glauber's normalized correlation functions. In contrast to our many-body entropy measures, single-particle entropy cannot capture these transitions.Comment: 11 pages, 7 figures, software available at http://ultracold.or

Particle Acceleration and the Production of Relativistic Outflows in Advection-Dominated Accretion Disks with Shocks

Relativistic outflows (jets) of matter are commonly observed from systems containing black holes. The strongest outflows occur in the radio-loud systems, in which the accretion disk is likely to have an advection-dominated structure. In these systems, it is clear that the binding energy of the accreting gas is emitted primarily in the form of particles rather than radiation. However, no comprehensive model for the disk structure and the associated outflows has yet been produced. In particular, none of the existing models establishes a direct physical connection between the presence of the outflows and the action of a microphysical acceleration mechanism operating in the disk. In this paper we explore the possibility that the relativistic protons powering the jet are accelerated at a standing, centrifugally-supported shock in the underlying accretion disk via the first-order Fermi mechanism. The theoretical analysis employed here parallels the early studies of cosmic-ray acceleration in supernova shock waves, and the particle acceleration and disk structure are treated in a coupled, self-consistent manner based on a rigorous mathematical approach. We find that first-order Fermi acceleration at standing shocks in advection-dominated disks proves to be a very efficient means for accelerating the jet particles. Using physical parameters appropriate for M87 and SgrA*, we verify that the jet kinetic luminosities computed using our model agree with estimates based on observations of the sources.Comment: accepted for publication in the Astrophysical Journa