12 We use Clebsch potentials and an action principle to derive a complete closed system of gauge-invariant equations for sound 13 superposed on a general background flow. Our system reduces to the Unruh [Phys. Rev. Lett. 46 (1981) 1351] and Pierce 14 [J. Acoust. Soc. Am. 87 (1990) 2292] wave equations when the flow is irrotational, or slowly varying. We illustrate our for-15 malism by applying it to waves propagating in a uniformly rotating fluid where the sound modes hybridize with inertial waves. 16

We give the quantum 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 U q (gl(2|1)). It is integrable in one dimension by means of the quantum inverse scattering method.

We investigate the propagation of electromagnetic waves through a static wormhole. It is shown that the problem can be reduced to a one dimensional Schrödinger-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.

We present an algebraic Bethe ansatz for the supersymmetric U model for correlated electrons on the unrestricted 4 L -dimensional electronic Hilbert space L nϭ1 C 4 ͑where L is the lattice length͒. The supersymmetry algebra of the model is the Lie superalgebra gl͑2͉1͒ and contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of gl͑2͉1͒. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice. ͓S0163-1829͑96͒03232-8͔

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., 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 Schrödinger operators. For the solution we derive here the potential of the Schrödinger 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 PT -symmetric wavefunctions defined on a contour in the complex plane.