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

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.

Nonequilibrium phase transition in surface growth

Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the introduction of an infinite series of higher-order nonlinear terms, these models exhibit, as function of a control parameter, a non-equilibrium phase transition between a kinetically rough phase with self-affine scaling and a phase that exhibits mound formation, slope selection and power-law coarsening.Comment: 7 pages, 4 .eps figures (Minor changes in text and references.

Low Energy Gamma-Ray Emission from Galactic Black Holes

X-ray observations of Galactic black holes (GBHs) such as Cygnus X-1 have greatly advanced the understanding of these objects. However, the vast majority of the observations have been restricted to energies below ~200 keV. The Compton Gamma-Ray Observatory (CGRO) allowed for the first time simultaneous observations at energies from ~25 keV up to >1 GeV. In particular, the BATSE experiment aboard CGRO was able to monitor low-energy gamma-ray emission from Cygnus X-1, as well as other GBHs, nearly continuously over a nine year period. Using the Enhanced BATSE Occultation Package (EBOP), light curves and spectra in the energy range 25–2000 keV have been obtained for six GBHs. Based on the spectra when the GBHs were in a high gamma-ray flux state, it is suggested that at least two different classes of GBHs exist. The first is characterized by a Comptonization spectrum below ~200 keV followed by a soft power law excess as exhibited by Cygnus X-1, GRO J0422+32, GRO J1719−24, and GX 339-4. The second class is characterized by simple power law spectrum in the full 25–2000 keV range, with no evidence for a Comptonization component, as exhibited by GRO J1655−40 and GRS 1915+105.Gamma-ray observations can serve as an important diagnostic in studying the physical processes around GBHs. More sensitive observations in the future at energies >250 keV will help answer questions regarding issues such as the nonthermal electron distribution, state transitions, and the connection to jets

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

On a nonstandard two-parametric quantum algebra and its connections with Up,q(gl(2))U_{p,q}(gl(2)) and Up,q(gl(1∣1))U_{p,q}(gl(1|1))

A quantum algebra $U_{p,q}(\zeta ,H,X_\pm )$ associated with a nonstandard $R$-matrix with two deformation parameters$(p,q)$ is studied and, in particular, its universal ${\cal R}$-matrix is derived using Reshetikhin's method. Explicit construction of the $(p,q)$-dependent nonstandard $R$-matrix is obtained through a coloured generalized boson realization of the universal ${\cal R}$-matrix of the standard $U_{p,q}(gl(2))$ corresponding to a nongeneric case. General finite dimensional coloured representation of the universal ${\cal R}$-matrix of $U_{p,q}(gl(2))$ is also derived. This representation, in nongeneric cases, becomes a source for various $(p,q)$-dependent nonstandard $R$-matrices. Superization of $U_{p,q}(\zeta , H,X_\pm )$ leads to the super-Hopf algebra $U_{p,q}(gl(1|1))$. A contraction procedure then yields a $(p,q)$-deformed super-Heisenberg algebra $U_{p,q}(sh(1))$ and its universal ${\cal R}$-matrix.Comment: 17pages, LaTeX, Preprint No. imsc-94/43 Revised version: A note added at the end of the paper correcting and clarifying the bibliograph

How glassy are orientational dynamics of rodlike molecules near the isotropic-nematic transition?

In an attempt to quantitatively characterize the recently observed slow dynamics in the isotropic and nematic phase of liquid crystals, we investigate the single-particle orientational dynamics of rodlike molecules across the isotropic-nematic transition in computer simulations of a family of model systems of thermotropic liquid crystals. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. In order to obtain a quantitative measure of glassy dynamics in line with the estbalished methods in supercooled liquids, we construct a relaxation time versus scaled inverse temperature plot, and demonstrate that one can indeed define a 'fragility index' for thermotropic liquid crystals, that depends on density and aspect ratio. The values of the fragility parameter are surprisingly in the range one observed for glass forming liquids. A plausible correlation between the energy landscape features and the observed fragility is discussed.Comment: 7 figures and 8 page

Coloured extension of GL_q(2) and its dual algebra

We address the problem of duality between the coloured extension of the quantised algebra of functions on a group and that of its quantised universal enveloping algebra i.e. its dual. In particular, we derive explicitly the algebra dual to the coloured extension of GL_q(2) using the coloured RLL relations and exhibit its Hopf structure. This leads to a coloured generalisation of the R-matrix procedure to construct a bicovariant differential calculus on the coloured version of GL_q(2). In addition, we also propose a coloured generalisation of the geometric approach to quantum group duality given by Sudbery and Dobrev.Comment: 10 pages LaTeX. Talk given at the "XXIII International Colloquium on Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna (Russia); to appear in the proceeding

Duality for Exotic Bialgebras

In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find the bialgebras which are in duality with these three exotic matrix bialgebras. We note that the $L-T$ duality of FRT is not sufficient for the construction of the bialgebras in duality. We find also the quantum planes corresponding to these bialgebras both by the Wess-Zumino R-matrix method and by Manin's method.Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeq