Spin waves in a one-dimensional spinor Bose gas

We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive delta-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or ``spin-charge'') separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.Comment: 4 pages, 1 figur

On the exactly solvable pairing models for bosons

We propose the new exactly solvable model for bosons corresponding to the attractive pairing interaction. Using the electrostatic analogy, the solution of this model in thermodynamic limit is found. The transition from the superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of excitations in the weak coupling regime to the incompressible phase with the gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page

Dynamical density-density correlations in the one-dimensional Bose gas

The zero-temperature dynamical structure factor of the one-dimensional Bose gas with delta-function interaction (Lieb-Liniger model) is computed using a hybrid theoretical/numerical method based on the exact Bethe Ansatz solution, which allows to interpolate continuously between the weakly-coupled Thomas-Fermi and strongly-coupled Tonks-Girardeau regimes. The results should be experimentally accessible with Bragg spectroscopy.Comment: 4 pages, 3 figures, published versio

New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case

We propose new formulas for eigenvectors of the Gaudin model in the \sl(3) case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula $| w_1, w_2) = \sum_{n=0}^\infty P^n/n! | w_1, w_2,0>$, where $w_1$, $w_2$ fulfil the standard well-know Bethe Ansatz equations

Kernel functions and B\"acklund transformations for relativistic Calogero-Moser and Toda systems

We obtain kernel functions associated with the quantum relativistic Toda systems, both for the periodic version and for the nonperiodic version with its dual. This involves taking limits of previously known results concerning kernel functions for the elliptic and hyperbolic relativistic Calogero-Moser systems. We show that the special kernel functions at issue admit a limit that yields generating functions of B\"acklund transformations for the classical relativistic Calogero-Moser and Toda systems. We also obtain the nonrelativistic counterparts of our results, which tie in with previous results in the literature.Comment: 76 page

Three-magnon problem for exactly rung-dimerized spin ladders: from general outlook to Bethe Ansatze

Three-magnon problem for exactly rung-dimerized spin ladder is brought up separately at all total spin sectors. At first a special duality transformation of the $\rm Schr\ddot odinger$ equation is found within general outlook. Then the problem is treated within Coordinate Bethe Ansatze. A straightforward approach is developed to obtain pure scattering states. At values S=0 and S=3 of total spin the $\rm Schr\ddot odinger$ equation has the form inherent in the $XXZ$ chain. For $S=1,2$ solvability holds only in five previously found {\it completely integrable} cases. Nevertheless a partial S=1 Bethe solution always exists even for general non integrable model. Pure scattering states for all total spin sectors are presented explicitly.Comment: 38 page

Gaudin models for gl(m|n)

Date of Acceptance: 16/04/2015We establish the basics of the Bethe ansatz for the Gaudin model associated to the Lie superalgebra gl(m|n). In particular, we prove the completeness of the Bethe ansatz in the case of tensor products of fundamental representations.Peer reviewedFinal Accepted Versio

On correlation functions of integrable models associated to the six-vertex R-matrix

We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum models. This generalized master equation allows us to obtain multiple integral representations for the correlation functions of these models. We apply this method to derive the density-density correlation functions of the quantum non-linear Schrodinger model.Comment: 21 page

Shear Effects in Non-Homogeneous Turbulence

Motivated by recent experimental and numerical results, a simple unifying picture of intermittency in turbulent shear flows is suggested. Integral Structure Functions (ISF), taking into account explicitly the shear intensity, are introduced on phenomenological grounds. ISF can exhibit a universal scaling behavior, independent of the shear intensity. This picture is in satisfactory agreement with both experimental and numerical data. Possible extension to convective turbulence and implication on closure conditions for Large-Eddy Simulation of non-homogeneous flows are briefly discussed.Comment: 4 pages, 5 figure

osp(1∣2)osp(1|2) off-shell Bethe ansatz equation with boundary terms

This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the $osp(1|2)$ vertex model with diagonal $K$-matrices. In this limit Gaudin's Hamiltonians with boundary terms are presented and diagonalized. Moreover, integral representations for correlation functions are realized to be solutions of the trigonometric Knizhnik-Zamoldchikov equations.Comment: 38 pages, minor revison, LaTe