12,002 research outputs found
Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the
main parts of the eigenfunctions of new solvable discrete quantum mechanical
systems. Their orthogonality weight functions consist of quantum dilogarithm
functions, which are a natural extension of the Euler gamma functions and the
q-gamma functions (q-shifted factorials). The dimensions of the orthogonal
spaces are finite. These q-orthogonal polynomials are expressed in terms of the
Askey-Wilson polynomials and their certain limit forms.Comment: 37 pages. Comments and references added. To appear in J.Math.Phy
Two-dimensional mapping of triaxial strain fields in a multiferroic BiFeO3 thin film using scanning x-ray microdiffraction
The dramatically enhanced polarizations and saturation magnetizations observed in the epitaxially constrained BiFeO3 (BFO) thin films with their pronounced grain-orientation dependence have attracted much attention and are attributed largely to the constrained in-plane strain. Thus, it is highly desirable to directly obtain information on the two-dimensional (2D) distribution of the in-plane strain and its correlation with the grain orientation of each corresponding microregion. Here the authors report a 2D quantitative mapping of the grain orientation and the local triaxial strain field in a 250 nm thick multiferroic BFO film using a synchrotron x-ray microdiffraction technique. This direct scanning measurement demonstrates that the deviatoric component of the in-plane strain tensor is between 5x10(-3) and 6x10(-3) and that the local triaxial strain is fairly well correlated with the grain orientation in that particular region. (c) 2007 American Institute of Physics.X1145Nsciescopu
Monte Carlo simulations of infinitely dilute solutions of amphiphilic diblock star copolymers
Single-chain Monte Carlo simulations of amphiphilic diblock star copolymers
were carried out in continuous space using implicit solvents. Two distinct
architectures were studied: stars with the hydrophobic blocks attached to the
core, and stars with the polar blocks attached to the core, with all arms being
of equal length. The ratio of the lengths of the hydrophobic block to the
length of the polar block was varied from 0 to 1. Stars with 3, 6, 9 or 12
arms, each of length 10, 15, 25, 50, 75 and 100 Kuhn segments were analysed.
Four distinct types of conformations were observed for these systems. These,
apart from studying the snapshots from the simulations, have been
quantitatively characterised in terms of the mean-squared radii of gyration,
mean-squared distances of monomers from the centre-of-mass, asphericity
indices, static scattering form factors in the Kratky representation as well as
the intra-chain monomer-monomer radial distribution functions.Comment: 12 pages, 11 ps figures. Accepted for publication in J. Chem. Phy
On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice
A new type of correlated disorder is shown to be responsible for the
appearance of extended electronic states in one-dimensional aperiodic systems
like the Thue-Morse lattice. Our analysis leads to an understanding of the
underlying reason for the extended states in this system, for which only
numerical evidence is available in the literature so far. The present work also
sheds light on the restrictive conditions under which the extended states are
supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in
Physical Review Letter
The BTZ black hole with a time-dependent boundary
The non-rotating BTZ solution is expressed in terms of coordinates that allow
for an arbitrary time-dependent scale factor in the boundary metric. We provide
explicit expressions for the coordinate transformation that generates this form
of the metric, and determine the regions of the complete Penrose diagram that
are convered by our parametrization. This construction is utilized in order to
compute the stress-energy tensor of the dual CFT on a time-dependent
background. We study in detail the expansion of radial null geodesic
congruences in the BTZ background for various forms of the scale factor of the
boundary metric. We also discuss the relevance of our construction for the
holographic calculation of the entanglement entropy of the dual CFT on
time-dependent backgrounds.Comment: 14 pages, 13 figures, title changed in journal, conformal diagrams
added, references added, final version to appear in Classical and Quantum
Gravit
Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
There is a pressing need for robust and straightforward methods to create
potentials for trapping Bose-Einstein condensates which are simultaneously
dynamic, fully arbitrary, and sufficiently stable to not heat the ultracold
gas. We show here how to accomplish these goals, using a rapidly-moving laser
beam that "paints" a time-averaged optical dipole potential in which we create
BECs in a variety of geometries, including toroids, ring lattices, and square
lattices. Matter wave interference patterns confirm that the trapped gas is a
condensate. As a simple illustration of dynamics, we show that the technique
can transform a toroidal condensate into a ring lattice and back into a toroid.
The technique is general and should work with any sufficiently polarizable
low-energy particles.Comment: Minor text changes and three references added. This is the final
version published in New Journal of Physic
Diffusive propagation of UHECR and the propagation theorem
We present a detailed analytical study of the propagation of ultra high
energy (UHE) particles in extragalactic magnetic fields. The crucial parameter
which affects the diffuse spectrum is the separation between sources. In the
case of a uniform distribution of sources with a separation between them much
smaller than all characteristic propagation lengths, the diffuse spectrum of
UHE particles has a {\em universal} form, independent of the mode of
propagation. This statement has a status of theorem. The proof is obtained
using the particle number conservation during propagation, and also using the
kinetic equation for the propagation of UHE particles. This theorem can be also
proved with the help of the diffusion equation. In particular, it is shown
numerically, how the diffuse fluxes converge to this universal spectrum, when
the separation between sources diminishes. We study also the analytic solution
of the diffusion equation in weak and strong magnetic fields with energy losses
taken into account. In the case of strong magnetic fields and for a separation
between sources large enough, the GZK cutoff can practically disappear, as it
has been found early in numerical simulations. In practice, however, the source
luminosities required are too large for this possibility.Comment: 16 pages, 13 eps figures, discussion of the absence of the GZK
cut-off in strong magnetic field added, a misprint in figure 6 corrected,
version accepted for publication in Ap
GALEX Observations of Diffuse UV Radiation at High Spatial Resolution from the Sandage Nebulosity
Using the GALEX ultraviolet imagers we have observed a region of nebulosity
first identified as starlight scattered by interstellar dust by Sandage (1976).
Apart from airglow and zodiacal emission, we have found a diffuse UV background
of between 500 and 800 \phunit in both the \galex FUV (1350 -- 1750 \AA) and
NUV (1750 -- 2850 \AA). Of this emission, up to 250 \phunit is due to \htwo
fluorescent emission in the FUV band; the remainder is consistent with
scattering from interstellar dust. We have estimated the optical constants to
be in the FUV and in the NUV, implying
highly forward scattering grains, plus an extragalactic contribution of as much
as 150 \phunit. These are the highest spatial resolution observations of the
diffuse UV background to date and show an intrinsic scatter beyond that
expected from instrumental noise alone. Further modeling is required to
understand the nature of this scatter and its implications for the ISM.Comment: Total 20 pages, Figures 9, Accepted for publication in Astrophysical
Journa
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