Exponential bounds for the probability deviations of sums of random fields

Non-asymptotic exponential upper bounds for the deviation probability for a sum of independent random fields are obtained under Bernstein's condition and assumptions formulated in terms of Kolmogorov's metric entropy. These estimations are constructive in the sense that all the constants involved are given explicitly. In the case of moderately large deviations, the upper bounds have optimal log-asymptotices. The exponential estimations are extended to the local and global continuity modulus for sums of independent samples of a random field

Nanoparticles as a possible moderator for an ultracold neutron source

Ultracold and very cold neutrons (UCN and VCN) interact strongly with nanoparticles due to the similarity of their wavelengths and nanoparticles sizes. We analyze the hypothesis that this interaction can provide efficient cooling of neutrons by ultracold nanoparticles at certain experimental conditions, thus increasing the density of UCN by many orders of magnitude. The present analytical and numerical description of the problem is limited to the model of independent nanoparticles at zero temperature. Constraints of application of this model are discussed

Integrable quadratic Hamiltonians on so(4) and so(3,1)

We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree.Comment: 16 page

SUSY vertex algebras and supercurves

This article is a continuation of math.QA/0603633 Given a strongly conformal SUSY vertex algebra V and a supercurve X we construct a vector bundle V_X on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle V_X, corresponding to a SUSY vertex algebra, carries the structure of a chiral algebra.Comment: 50 page

Systematic approach to cyclic orbifolds

We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions of conformal field theory and enables us to find the orbifold characters and their modular transformation properties.Comment: 39 pages, LaTeX. v2,3: references added. v4: typos correcte

Parameters of the Effective Singlet-Triplet Model for Band Structure of High-TcT_c Cuprates by Different Approaches

The present paper covers the problem of parameters determination for High-$T_c$ superconductive copper oxides. Different approaches, {\it ab initio} LDA and LDA+U calculations and Generalized Tight-Binding (GTB) method for strongly correlated electron systems, are used to calculate hopping and exchange parameters of the effective singlet-triplet model for $CuO_2$-layer. The resulting parameters are in remarkably good agreement with each other and with parameters extracted from experiment. This set of parameters is proposed for proper quantitative description of physics of hole doped High-$T_c$ cuprates in the framework of effective models.Comment: PACS 74.72.h; 74.20.z; 74.25.Jb; 31.15.A

Leptonic Decays of the W-Boson in a Strong Electromagnetic Field

The probability of W-boson decay into a lepton and a neutrino in a strong electromagnetic field is calculated. On the basis of the method for deriving exact solutions to relativistic wave equations for charged particles, an exact analytic expression is obtained for the partial W-decay width at an arbitrary value of the external field strength. It is found that, in the region of comparatively weak fields, field-induced corrections to the standard decay width of the W-boson in a vacuum are about a few percent. In these conditions at first we observe the decrease of the W-boson partial decay width with the increase of the external field strength parameter. At absolute minimum the W-width deviates from the corresponding vacuum value by a factor 0,926. Then with further augmentation of the background field intensity the W-boson decay width grows monotonously. In superstrong fields the partial W-width is greater than the corresponding one in vacuum in a dozen of times.Comment: LaTex file, 19 pages, 2 Postscript figur