890 research outputs found
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
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