Maxwell-Bloch equation and Correlation function for penetrable Bose gas

We consider the quantum nonlinear Schr\"odinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation for correlation functions simplifies in the small mass limit of the Bose particle. In this limit we describe the correlation functions by the vacuum expectation value of a boson-valued solution for Maxwell-Bloch differential equation. We evaluate long-distance asymptotics of correlation functions in the small mass limit.Comment: LaTEX file, 20 pages, to appear J. Phys. A (1997

Six - Vertex Model with Domain wall boundary conditions. Variable inhomogeneities

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of inhomogeneities. For certain choices of the inhomogeneities we study arrow correlation functions on the horizontal line going through the centre. In particular we obtain a multiple integral representation for the emptiness formation probability that generalizes the known formul\ae for XXZ antiferromagnets.Comment: 12 pages, 1 figur

Integral equations for the correlation functions of the quantum one-dimensional Bose gas

The large time and long distance behavior of the temperature correlation functions of the quantum one-dimensional Bose gas is considered. We obtain integral equations, which solutions describe the asymptotics. These equations are closely related to the thermodynamic Bethe Ansatz equations. In the low temperature limit the solutions of these equations are given in terms of observables of the model.Comment: 22 pages, Latex, no figure

The New Identity for the Scattering Matrx of Exactly Solvable Models

We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one dimensional Bose gas and XXZ Heisenberg spin chain.Comment: 7 pages, Latex, no figure

Determinant representation for dynamical correlation functions of the Quantum nonlinear Schr\"odinger equation

The foundation for the theory of correlation functions of exactly solvable models is determinant representation. Determinant representation permit to describe correlation functions by classical completely integrable differential equations [Barough, McCoy, Wu]. In this paper we show that determinant represents works not only for free fermionic models. We obtained determinant representation for the correlation function $$ of the quantum nonlinear Schr\"odinger equation, out of free fermionic point. In the forthcoming publications we shall derive completely integrable equation and asymptotic for the quantum correlation function of this model of interacting fermions.Comment: LaTEX file, 35 pages, to appear in C.M.P. (1997