Katrina E. Hibberd

Integrable electron model with correlated hopping and quantum supersymmetry

Abstract We give the q-deformed analogue of a recently introduced electron model which generalizes the Hubbard model with additional correlated hopping terms and electron pair hopping. The model contains two independent parameters and is invariant with respect to the quantum superalgebra Uq(gl(2|1)). It is shown to be integrable in one dimension by means of the quantum inverse scattering method.

Wave equation for sound in fluids with vorticity

We use Clebsch potentials and an action principle to derive a complete closed system of gauge-invariant equations for sound superposed on a general background flow. Our system reduces to the Unruh [Phys. Rev. Lett. 46 (1981) 1351] and Pierce [J. Acoust. Soc. Am. 87 (1990) 2292] wave equations when the flow is irrotational, or slowly varying. We illustrate our formalism by applying it to waves propagating in a uniformly rotating fluid where the sound modes hybridize with inertial waves.

Quantum spin ladder systems associated with su(2|2)

Two integrable quantum spin ladder systems will be introduced associated with the fundamental su(2 \2) solution of the Yang-Baxter equation. The first model is a generalized quantum Ising system with Ising rung interactions. In the second model the addition of extra interactions allows us to impose Heisenberg rung interactions without violating integrability. The existence of a Bethe ansatz solution for both models allows us to investigate the elementary excitations for antiferromagnetic rung couplings. We find that the first model does not show a gap whilst in the second case there is a gap for all positive values of the rung coupling.

INTEGRABLE COUPLING IN A MODEL FOR JOSEPHSON TUNNELING BETWEEN NON-IDENTICAL BCS SYSTEMS

We extend a recent construction for an integrable model describing Josephson tunneling between identical BCS systems to the case where the BCS systems have different single particle energy levels. The exact solution of this generalized model is obtained through the Bethe ansatz.

Electromagnetic waves in a wormhole geometry

We investigate the propagation of electromagnetic waves through a static wormhole. It is shown that the problem can be reduced to a one dimensional Schrodinger-like equation with a barrier-type potential. Using numerical methods, we calculate the transmission coefficient as a function of the energy. We also discuss the polarization of the outgoing radiation due to this gravitational scattering. ©2000 The American Physical Society

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Bethe Ansatz Solutions of the Bose-Hubbard Dimer ?

The Bose-Hubbard dimer Hamiltonian is a simple yet effective model for descri- bing tunneling phenomena of Bose-Einstein condensates. One of the significant mathema- tical properties of the model is that it can be exactly solved by Bethe ansatz methods. Here we review the known exact solutions, highlighting the contributions of V.B. Kuznetsov to this field. Two of the exact solutions arise in the context of the Quantum Inverse Scattering Method, while the third solution uses a differential operator realisation of the su(2) Lie algebra.

Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter.

Integrable open supersymmetric U model with boundary impurity

An integrable version of the supersymmetric U model with open boundary conditions and an impurity situated at one end of the chain is introduced. The model is solved through the nested algebraic Bethe ansatz method so that the Bethe ansatz equations are obtained

BETHE ANSATZ SOLUTION OF THE CLOSED ANISOTROPIC SUPERSYMMETRIC U MODEL WITH QUANTUM SUPERSYMMETRY

The nested algebraic Bethe Ansatz is presented for the anisotropic supersymmetric U> model maintaining quantum supersymmetry. The Bethe Ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for the energy is given.