774 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

### 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

### A nonlinear indentity for the scattering phase of integrable models

A nonlinear identity for the scattering phase of quantum integrable models is
proved.Comment: 5 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

### 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

### Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture

We consider one-dimensional quantum spin chain, which is called XX model, XX0
model or isotropic XY model in a transverse magnetic field. We study the model
on the infinite lattice at zero temperature. We are interested in the entropy
of a subsystem [a block of L neighboring spins]. It describes entanglement of
the block with the rest of the ground state.
G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev showed that for large blocks
the entropy scales logarithmically. We prove the logarithmic formula for the
leading term and calculate the next term.
We discovered that the dependence on the magnetic field interacting with
spins is very simple: the magnetic field effectively reduce the size of the
subsystem.
We also calculate entropy of a subsystem of a small size. We also evaluated
Renyi and Tsallis entropies of the subsystem. We represented the entropy in
terms of a Toeplitz determinant and calculated the asymptotic analytically.Comment: LATEX, 17 pages, 1 fi

- …