Generalized entropy of the Heisenberg spin chain

We consider the XY quantum spin chain in a transverse magnetic field. We consider the Rényi entropy of a block of neighboring spins at zero temperature on an infinite lattice. The Rényi entropy is essentially the trace of some power α of the density matrix of the block. We calculate the entropy of the large block in terms of Klein’s elliptic λ-function. We study the limit entropy as a function of its parameter α. We show that the Rényi entropy is essentially an automorphic function with respect to a certain subgroup of the modular group. Using this, we derive the transformation properties of the Rényi entropy under the map α → α ⁻¹ .     

Universality of the one-dimensional Bose gas with delta interaction

We consider several models of interacting bosons in a one-dimensional lattice. Some of them are not integrable like the Bose-Hubbard others are integrable. At low density all of these models can be described by the Bose gas with delta interaction. The lattice corrections corresponding to the different models are contrasted.     

Kinetics of the thermal decomposition of bis(2,2-dinitropropyl)-N-fluoroamine

The kinetics of the thermal decomposition of bis(2,2-dinitropropyl)-N-fluoroamine are studied in the liquid phase. The reaction is autocatalytic in a melt. In dilute solution, the reaction rate is described by the first-order law. It is tens of times faster in polar sulfolan than in weakly polar dimethyl phthalate. A mechanism of the decomposition involving the formation of a cyclic transition state at the first, limiting stage of the process is suggested.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 874–877, May, 1995.This work was financially supported by the Russian Foundation for Basic Research (Project No. 94-03-08103).     

Calculation of norms of Bethe wave functions

A class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered. Eigenfunctions of the Hamiltonians are known for these models. Norms of these eigenfunctions in the finite box are calculated in the present paper. These models include in particular the quantum nonlinear Schrödinger equation and the HeisenbergXXZ model.     

Critical properties and correlation functions of the eight-vertex model on a quasicrystal

It is shown that the critical indices of completely integrable spin models in quasi-crystals coincide with the critical indices of the corresponding models in crystals. A classification is given of thermodynamic phases of the eight-vertex model and the pair correlation function of the Ising model in a quasicrystal is found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 161, pp. 13–23, 1987.     

Lattice regularizations of two-dimensional quantum-field models

Completely integrable lattice versions of the nonlinear Schrödinger equation and the sine-Gordon model are formulated in the quantum and classical cases. The group meaning of exact L-operators is discussed, and local Hamiltonians are constructed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 120, pp. 75–91, 1982.We thank L. D. Faddeev for useful discussions.