928 research outputs found
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 , where , 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 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 equation has the form inherent in the
chain. For 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
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 vertex model with diagonal
-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
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