Norms of bound states

The formula for the norms of the Bethe wave functions in the form of a Jacobian plays an important role in the computation of the correlation functions. In the present paper this formula is generalized to the case of bound states.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 146, pp. 20–30, 1985.     

Synthesis and structure of 6-azido-2,4-bis(2,2,2-trinitroethylamino)-1,3,5-triazine and its <Emphasis Type="Italic">N</Emphasis>-nitro derivatives

Methods were developed for the synthesis of 6-azido-2,4-bis(2,2,2-trinitroethylamino)- 1,3,5-triazine and its N-nitro derivatives (6-azido-2,4-bis(2,2,2-trinitroethyl)nitramino-1,3,5-triazine and 6-azido-2-(2,2,2-trinitroethylamino)-4-(2,2,2-trinitroethyl)nitramino-1,3,5-triazine) containing combinations of azido, trinitroethyl, and nitramine groups. These compounds are of interest as components of energetic composites. The molecular and crystal structures of 6-azido-2,4-bis(2,2,2-trinitroethylamino)-1,3,5-triazine and 6-azido-2,4-bis(2,2,2-trinitroethyl) nitramino-1,3,5-triazine were studied by X-ray diffraction and NMR spectroscopy.     

Correlation functions of the one-dimensional Hubbard model

Conclusions We have investigated the critical behavior of the Hubbard model with attraction. To investigate the critical behavior of the model with repulsion, it is sufficient to use a unitary electron-hole transformation [3,8], and then the SCP correlation function will correspond to the spin-wave correlation function (the parameters of the models can be readily recalculated).The quasione-dimensional generalization of the investigated system can be used as a model of a high-temperature superconductor with chemical pairing mechanism [16,25].Leningrad Branch, V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 3, pp. 331–348, March, 1990.     

Elimination reactions of N,C-difluorides

Hydrogen fluoride was eliminated from N,C-difluorinated derivatives of bis(polynitroalkyl)amines by the action of alkanols. Previously unreported -fluoropolynitroalkylaldimines were obtained.Institute of Chemical Physics, Russian Academy of Sciences, 142432 Chernogolovka. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 742–743, March, 1992.     

Quantum Spin Chain,Toeplitz Determinants and the Fisher—Hartwig Conjecture

We consider the one-dimensional quantum spin chain, which is called the XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We are mainly interested in the entropy of a block of Lneighboring spins at zero temperature and of an infinite system. We represent the entropy in terms of a Toeplitz determinant and calculate the asymptotic analytically. We derive the first two terms of the asymptotic decomposition. Interestingly, these two terms of decomposition clearly show a length scale related to the field h.     

Effect of polymorphic phase transitions on stability of energetic compounds. Thermal transformations of 2,4,6-tris(2,2,2-trinitroethylnitramino)-1,3,5-triazine

Russian Chemical Bulletin - The kinetics of thermal transformations of the energetic compound 2,4,6-tris(2,2,2- trinitroethylnitramino)-1,3,5-triazine (1) and products of this reaction were studied...     

Correlation functions for the Heisenberg XXZ-antiferromagnet

The general method for calculation of correlation functions in integrable quantum models has been given in papers [1, 2]. The correlation function of the third components of local spins for the Heisenberg one-dimensionalXXZ-antiferromagnet is calculated in this paper. The answer is a series which gives, in particular, an improved version of the usual perturbative expansion in the anisotropy parameter. The remarkable property of the series obtained is that the long-distance asymptotics of the correlator is given already by the first term. The arguments are given in favour of the convergence of the series.     

Dual field formulation of quantum integrable models

Equal time correlators are studied in completely integrable models. The main example is the quantum non-linear Schrödinger equation. Introduction of an auxiliary Fock space permits us to represent the generating functional of correlators in the form of a determinant of the integral operator.     

The Pauli principle for one-dimensional bosons and the algebraic bethe ansatz

To construct the physical vacuum in completely integrable models of one-dimensional boson fields, it is essential that the momenta of all particles be distinct. A proof is present that they actually are distinct.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 120, pp. 69–74, 1982.In conclusion we thank L. D. Fadeev for useful discussions.