2 research outputs found
Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations
We calculate exactly matrix elements between states that are not eigenstates
of the quantum XY model for general anisotropy. Such quantities therefore
describe non equilibrium properties of the system; the Hamiltonian does not
contain any time dependence. These matrix elements are expressed as a sum of
Pfaffians. For single particle excitations on the ground state the Pfaffians in
the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of
refs. modifie
Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins
In this review we demonstrate how the algebraic Bethe ansatz is used for the
calculation of the energy spectra and form factors (operator matrix elements in
the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As
examples we apply the theory to several models of current interest in the study
of Bose-Einstein condensates, which have been successfully created using
ultracold dilute atomic gases. The first model we introduce describes Josephson
tunneling between two coupled Bose-Einstein condensates. It can be used not
only for the study of tunneling between condensates of atomic gases, but for
solid state Josephson junctions and coupled Cooper pair boxes. The theory is
also applicable to models of atomic-molecular Bose-Einstein condensates, with
two examples given and analysed. Additionally, these same two models are
relevant to studies in quantum optics. Finally, we discuss the model of
Bardeen, Cooper and Schrieffer in this framework, which is appropriate for
systems of ultracold fermionic atomic gases, as well as being applicable for
the description of superconducting correlations in metallic grains with
nanoscale dimensions. In applying all of the above models to physical
situations, the need for an exact analysis of small scale systems is
established due to large quantum fluctuations which render mean-field
approaches inaccurate.Comment: 49 pages, 1 figure, invited review for J. Phys. A., published version
available at http://stacks.iop.org/JPhysA/36/R6