Classical and Quantum Nonultralocal Systems on the Lattice

We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix . A nonultralocal quantum algebras on the lattices for these systems are constructed.For some class of such algebras an ultralocalization procedure is proposed.The technique of the modified Bethe-Anzatz for these algebras is developed.This technique is applied to the nonlinear sigma model problem.Comment: 33 pp. Latex. The file is resubmitted since it was spoiled during transmissio

Probability of the resistive state formation caused by absorption of a single-photon in current-carrying superconducting nano-strips

We have studied supercurrent-assisted formation of the resistive state in nano-structured Nb and NbN superconducting films after absorption of a single photon. In amorphous narrow NbN strips the probability of the resistive state formation has a pronounced spectral cut-off. The corresponding threshold photon energy decreases with the bias current. Analysis of the experimental data in the framework of the generalized hot-spot model suggests that the quantum yield for near-infrared photons increases faster than the photon nergy. Relaxation of the resistive state depends on the photon energy making the phenomenon feasible for the development of energy resolving single-photon detectors.Comment: 9 pages, 9 figures, submitted to Eur. Phys. Journa

Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General Semisimple Case

The paper is the sequel to q-alg/9704011. We extend the Drinfeld-Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic deformation of the Lie bialgebra structure on the associated loop algebra. The related classical r-matrix is explicitly described in terms of the Coxeter transformation. We also present a cross-section theorem for q-gauge transformations which generalizes a theorem due to R.Steinberg.Comment: 19 pp., AMS-LaTeX. The paper replaces a temporarily withdrawn text; the first part (written by E. Frenkel, N. Reshetikhin, and M. A. Semenov-Tian-Shansky) is available as q-alg/970401