Spatiospectral concentration on a sphere

We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere, or, alternatively, of strictly spacelimited functions that are optimally concentrated within the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology and numerical analysis. The spherical Slepian functions can be found either by solving an algebraic eigenvalue problem in the spectral domain or by solving a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a Sturm-Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small concentration region and a large spherical harmonic bandwidth the spherical concentration problem approaches its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.Comment: 48 pages, 17 figures. Submitted to SIAM Review, August 24th, 200

The Stellar Content Near the Galactic Center

High angular resolution J, H, K, and L' images are used to investigate the stellar content within 6 arcsec of SgrA*. The data, which are complete to K ~ 16, are the deepest multicolor observations of the region published to date.Comment: 34 pages, including 12 figure

Universal parametric correlations in the transmission eigenvalue spectra of disordered conductors

We study the response of the transmission eigenvalue spectrum of disordered metallic conductors to an arbitrary external perturbation. For systems without time-reversal symmetry we find an exact non-perturbative solution for the two-point correlation function, which exhibits a new kind of universal behavior characteristic of disordered conductors. Systems with orthogonal and symplectic symmetries are studied in the hydrodynamic regime.Comment: 10 pages, written in plain TeX, Preprint OUTP-93-36S (University of Oxford), to appear in Phys. Rev. B (Rapid Communication

Polaritons and Pairing Phenomena in Bose--Hubbard Mixtures

Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the problem of a two-band Bose--Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the non-trivial interplay between Mott insulating behavior and superfluidity. The model displays a global U(1) X U(1) symmetry which supports the coexistence of Mott insulating and superfluid phases, and yields a rich phase diagram with multicritical points. This symmetry property is shared by several other problems of current experimental interest, including two-component Bose gases in optical lattices, and the bosonic BEC-BCS crossover problem for atom-molecule mixtures induced by a Feshbach resonance. We corroborate our findings by numerical simulations.Comment: 4 pages, 3 figure

Single-particle Green's functions of the Calogero-Sutherland model at couplings \lambda = 1/2, 1, and 2

At coupling strengths lambda = 1/2, 1, or 2, the Calogero-Sutherland model (CSM) is related to Brownian motion in a Wigner-Dyson random matrix ensemble with orthogonal, unitary, or symplectic symmetry. Using this relation in conjunction with superanalytic techniques developed in mesoscopic conductor physics, we derive an exact integral representation for the CSM two-particle Green's function in the thermodynamic limit. Simple closed expressions for the single-particle Green's functions are extracted by separation of points. For the advanced part, where a particle is added to the ground state and later removed, a sum of two contributions is found: the expected one with just one particle excitation present, plus an extra term arising from fractionalization of the single particle into a number of elementary particle and hole excitations.Comment: 19 REVTeX page

Ising Deconfinement Transition Between Feshbach-Resonant Superfluids

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group (DMRG) and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary.Comment: 4 pages, 4 figure

Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903

Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics

One-dimensional model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green's function (hole propagator) at any rational interaction coupling constant $\lambda = p/q$ are obtained and used to show clear evidences of the fractional statistics. Motifs representing the eigenstates of the model are also constructed and used to reveal the fractional {\it exclusion} statistics (in the sense of Haldane's ``Generalized Pauli Exclusion Principle''). This model is also endowed with a natural {\it exchange } statistics (1D analog of 2D braiding statistics) compatible with the {\it exclusion} statistics. (Submitted to PRL on April 18, 1994)Comment: Revtex 11 pages, IASSNS-HEP-94/27 (April 18, 1994