Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation

We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of formation of a ferromagnetic string in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of EFP in the inhomogeneous case. It is based on quantum Knizhnik-Zamolodchikov equation. We evalauted EFP for strings of the length six in the inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations to number theory. We also make a conjecture about a general structure of EFP for arbitrary lenght of the string \.Comment: LATEX file, 23 pages, 21 reference

On the calculation of finite-gap solutions of the KdV equation

A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these solutions in the form of rational functions of the elliptic Weierstrass function. The calculation of initial elliptic finite-gap solutions is reduced to the solution of the finite-band equations with respect to the parameters of the representation. The time evolution of these solutions is described via the dynamic equations of their poles, integrated with the help of the finite-gap equations. The proposed approach is applied by calculating the elliptic 1-, 2- and 3-gap solutions of the KdV equations

The Yangian symmetry of the Hubbard Model

We discovered new hidden symmetry of the one-dimensional Hubbard model. We showthat the one-dimensional Hubbard model on the infinite chain has the infinite-dimensional algebra of symmetries. This algebra is a direct sum of two $sl(2)$-Yangians. This $Y(sl(2)) \oplus Y(sl(2))$ symmetry is an extension of the well-known $sl(2) \oplus sl(2)$ . The deformation parameters of the Yangians are equal up to the signs to the coupling constant of the Hubbard model hamiltonian.Comment: 7 pages, ITP-SB-93-6

Surface deep profile synchrotron studies of mechanically modified top-down silicon nanowires array using ultrasoft X-ray absorption near edge structure spectroscopy

Atomic, electronic structure and composition of top-down metal-assisted wet-chemically etched silicon nanowires were studied by synchrotron radiation based X-ray absorption near edge structure technique. Local surrounding of the silicon and oxygen atoms in silicon nanowires array was studied on as-prepared nanostructured surfaces (atop part of nanowires) and their bulk part after, first time applied, in-situ mechanical removal atop part of the formed silicon nanowires. Silicon suboxides together with disturbed silicon dioxide were found in the composition of the formed arrays that affects the electronic structure of silicon nanowires. The results obtained by us convincingly testify to the homogeneity of the phase composition of the side walls of silicon nanowires and the electronic structure in the entire length of the nanowire. The controlled formation of the silicon nanowires array may lead to smart engineering of its atomic and electronic structure that influences the exploiting strategy of metal-assisted wet-chemically etched silicon nanowires as universal matrices for different applications

TWO-PHASE FLOW STUDIES IN NUCLEAR POWER PLANT PRIMARY CIRCUITS USING THE THREE-DIMENSIONAL THERMAL-HYDRAULIC CODE BAGIRA.

In this paper we present recent results of the application of the thermal-hydraulic code BAGIRA to the analysis of complex two-phase flows in nuclear power plants primary loops. In particular, we performed benchmark numerical simulation of an integral LOCA experiment performed on a test facility modeling the primary circuit of VVER-1000. In addition, we have also analyzed the flow patterns in the VVER-1000 steam generator vessel for stationary and transient operation regimes. For both of these experiments we have compared the numerical results with measured data. Finally, we demonstrate the capabilities of BAGIRA by modeling a hypothetical severe accident for a VVER-1000 type nuclear reactor. The numerical analysis, which modeled all stages of the hypothetical severe accident up to the complete ablation of the reactor cavity bottom, shows the importance of multi-dimensional flow effects

Determinant Representations of Correlation Functions for the Supersymmetric t-J Model

Working in the $F$-basis provided by the factorizing $F$-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.Comment: Latex File, 41 pages, no figure; V2: minor typos corrected, V3: This version will appear in Commun. Math. Phy