Quantum fluctuations of a vortex in an optical lattice

Using a variational ansatz for the wave function of the Bose-Einstein condensate, we develop a quantum theory of vortices and quadrupole modes in a one-dimensional optical lattice. We study the coupling between the quadrupole modes and Kelvin modes, which turns out to be formally analogous to the theory of parametric processes in quantum optics. This leads to the possibility of squeezing vortices. We solve the quantum multimode problem for the Kelvin modes and quadrupole modes numerically and find properties that cannot be explained with a simple linear-response theory.Comment: final version, minor change

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

Model fluid in a porous medium: results for a Bethe lattice

We consider a lattice gas with quenched impurities or `quenched-annealed binary mixture' on the Bethe lattice. The quenched part represents a porous matrix in which the (annealed) lattice gas resides. This model features the 3 main factors of fluids in random porous media: wetting, randomness and confinement. The recursive character of the Bethe lattice enables an exact treatment, whose key ingredient is an integral equation yielding the one-particle effective field distribution. Our analysis shows that this distribution consists of two essentially different parts. The first one is a continuous spectrum and corresponds to the macroscopic volume accessible to the fluid, the second is discrete and comes from finite closed cavities in the porous medium. Those closed cavities are in equilibrium with the bulk fluid within the grand canonical ensemble we use, but are inaccessible in real experimental situations. Fortunately, we are able to isolate their contributions. Separation of the discrete spectrum facilitates also the numerical solution of the main equation. The numerical calculations show that the continuous spectrum becomes more and more rough as the temperature decreases, and this limits the accuracy of the solution at low temperatures.Comment: 13 pages, 12 figure

Spiked oscillators: exact solution

A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger equation. The procedure is applied to three familiar examples of spiked oscillators

U(2) and Maximal Mixing of nu_{mu}

A U(2) flavor symmetry can successfully describe the charged fermion masses and mixings, and supress SUSY FCNC processes, making it a viable candidate for a theory of flavor. We show that a direct application of this U(2) flavor symmetry automatically predicts a mixing of 45 degrees for nu_mu to nu_s, where nu_s is a light, right-handed state. The introduction of an additional flavor symmetry acting on the right-handed neutrinos makes the model phenomenologically viable, explaining the solar neutrino deficit as well as the atmospheric neutrino anomaly, while giving a potential hot dark matter candidate and retaining the theory's predictivity in the quark sector.Comment: 20 pages, 1 figur

General energy bounds for systems of bosons with soft cores

We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and lower bound formulas for the N-particle ground-state energy in arbitrary spatial dimensions d > 2 for the two cases p = 2 and p = -1. It is demonstrated that the upper bound can be systematically improved with the aid of a special large-N limit in collective field theory

A basis for variational calculations in d dimensions

In this paper we derive expressions for matrix elements (\phi_i,H\phi_j) for the Hamiltonian H=-\Delta+\sum_q a(q)r^q in d > 1 dimensions. The basis functions in each angular momentum subspace are of the form phi_i(r)=r^{i+1+(t-d)/2}e^{-r^p/2}, i >= 0, p > 0, t > 0. The matrix elements are given in terms of the Gamma function for all d. The significance of the parameters t and p and scale s are discussed. Applications to a variety of potentials are presented, including potentials with singular repulsive terms of the form b/r^a, a,b > 0, perturbed Coulomb potentials -D/r + B r + Ar^2, and potentials with weak repulsive terms, such as -g r^2 + r^4, g > 0.Comment: 22 page