Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : U_q(sl(3)) and Beyond,

A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a q - difference realization of U_q(sl(n)) in terms of n(n-1)/2 commuting variables and depending on n-1 complex representation parameters r_i, is constructed. From this realization lowest weight modules (LWM) are obtained which are studied in detail for the case n=3 (the well known n=2 case is also recovered). All reducible LWM are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given. This also gives a classification of the quasi-exactly solvable operators in the present setting. The invariant subspaces are obtained as solutions of certain invariant q - difference equations, i.e., these are kernels of invariant q - difference operators, which are also explicitly given. Such operators were not used until now in the theory of polynomial solutions. Finally the states in all subrepresentations are depicted graphically via the so called Newton diagrams.Comment: uuencoded Z-compressed .tar file containing two ps files

Pair creation and plasma oscillations

We describe aspects of particle creation in strong fields using a quantum kinetic equation with a relaxation-time approximation to the collision term. The strong electric background field is determined by solving Maxwell's equation in tandem with the Vlasov equation. Plasma oscillations appear as a result of feedback between the background field and the field generated by the particles produced. The plasma frequency depends on the strength of the initial background field and the collision frequency, and is sensitive to the necessary momentum-dependence of dressed-parton masses.Comment: 11 pages, revteX, epsfig.sty, 5 figures; Proceedings of 'Quark Matter in Astro- and Particlephysics', a workshop at the University of Rostock, Germany, November 27 - 29, 2000. Eds. D. Blaschke, G. Burau, S.M. Schmid

Mesoscopic to universal crossover of transmission phase of multi-level quantum dots

Transmission phase \alpha measurements of many-electron quantum dots (small mean level spacing \delta) revealed universal phase lapses by \pi between consecutive resonances. In contrast, for dots with only a few electrons (large \delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multi-level quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of \alpha for small \delta follows from Fano-type antiresonances of the renormalized single-particle levels.Comment: 4 pages, version accepted for publication in PR

String amplitudes in arbitrary dimensions

We calculate gravitational dressed tachyon correlators in non critcal dimensions. The 2D gravity part of our theory is constrained to constant curvature. Then scaling dimensions of gravitational dressed vertex operators are equal to their bare conformal dimensions. Considering the model as d+2 dimensional critical string we calculate poles of generalized Shapiro-Virasoro amplitudes.Comment: 14 page

Influence of contacts on the microwave response of a two-dimensional electron stripe

Electromagnetic response of a finite-width two-dimensional electron stripe with attached metallic side contacts is theoretically studied. It is shown that contacts substantially influence the position, the linewidth, and the amplitude of plasmon-polariton resonances in the stripe. In finite magnetic fields, absorption of the wave with the inactive circular polarization (which is not absorbed in an infinite system without contacts) may become larger than that of the wave with the active polarization. The results are discussed in view of recent microwave experiments in two-dimensional electron systems.Comment: 13 pages, incl. 9 figures, the paper has been substantially modified and extended, new results have been added. Accepted for publication in Phys. Rev.