Coherent Orthogonal Polynomials

We discuss as a fundamental characteristic of orthogonal polynomials like the existence of a Lie algebra behind them, can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we put thus --in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions-- Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis ${|x>}$, for an alternative countable basis ${|n>}$. The matrix elements that relate these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine a unitary representation of a non-compact Lie algebra, whose second order Casimir ${\cal C}$ gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl-Heisenberg algebra $h(1)$ with ${\cal C}=0$ for Hermite polynomials and $su(1,1)$ with ${\cal C}=-1/4$ for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the ${\cal L}^2$ functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space ${\cal L}^2$ and, in particular, generalized coherent polynomials are thus obtained.Comment: 11 page

The Effects of Quantum Entropy on the Bag Constant

The effects of quantum entropy on the bag constant are studied at low temperatures and small chemical potentials. The inclusion of the quantum entropy of the quarks in the equation of state provides the hadronic bag with an additional heat which causes a decrease in the effective latent heat inside the bag. We have considered two types of baryonic bags, $\Delta$ and $\Omega^-$. In both cases we have found that the bag constant without the quantum entropy almost does not change with the temperature and the quark chemical potential. The contribution from the quantum entropy to the equation of state clearly decreases the value of the bag constant.Comment: 7 pages, 2 figures (two parts each

Fungal Biomass Responses in Oil Perturbated Tundra at Barrow, Alaska

The effects of two Prudhoe Bay crude oil treatments of 5 and 12 l/square m on fungal hyphae/gm dry wt of soil and on the grams of mycelium/square m were followed in polygonal tundra for three seasons. A significant depressing effect of oil on fungal hyphae was evident over three seasons. However, no significant difference between oil treatments was recorded. The moisture content of the soil appeared to influence the mobility of the oil. Shifts occur in fungal populations in the presence of oil and the presence of oil biodegradation by filamentous fungi was detected. The influence of bulk density on fungal populations and the penetration of oil into tundra soil is discussed

Uniform semiclassical wave function for coherent 2D electron flow

We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The formation of branches has been explained by classical arguments, but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes in the phase space. In this paper, expansion in terms of "replacement manifolds" is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and applied to calculate uniform wave functions for a quantum-map model of coherent flow through a 2DEG. Finally, the quantum-map approximation is dropped and the method is shown to work for a continuous-time model as well.Comment: 9 pages, 7 figure