8,580 research outputs found
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
COMPUTATIONAL STABILITY AND TIME TRUNCATION OF COUPLED NONLINEAR EQUATIONS WITH EXACT SOLUTIONS
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 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
- …