2,128 research outputs found
Comparison theorems for the position-dependent mass Schroedinger equation
The following comparison rules for the discrete spectrum of the
position-dependent mass (PDM) Schroedinger equation are established. (i) If a
constant mass and a PDM are ordered everywhere, that is either
or , then the corresponding eigenvalues of the
constant-mass Hamiltonian and of the PDM Hamiltonian with the same potential
and the BenDaniel-Duke ambiguity parameters are ordered. (ii) The corresponding
eigenvalues of PDM Hamiltonians with the different sets of ambiguity parameters
are ordered if has a definite sign. We prove these
statements by using the Hellmann-Feynman theorem and offer examples of their
application.Comment: 11 pages, 2 figure
Cosmic Rays from Gamma Ray Bursts in the Galaxy
The rate of terrestrial irradiation events by galactic gamma-ray bursts
(GRBs) is estimated using recent standard-energy results. We assume that GRBs
accelerate high-energy cosmic rays, and present results of three-dimensional
simulations of cosmic rays moving in the Galactic magnetic field and diffusing
through pitch-angle scattering. An on-axis GRB extinction event begins with a
powerful prompt gamma-ray and neutron pulse, followed by a longer-lived phase
from cosmic-ray protons and neutron-decay protons that diffuse towards Earth.
Our results force a reinterpretation of reported ~ 10^{18} eV cosmic-ray
anisotropies and offer a rigorous test of the model where high-energy cosmic
rays originate from GRBs, which will soon be tested with the Auger Observatory.Comment: 9 pages, 4 figures, ApJ Letters, in press. Clarified limit of
test-particle approximation, prediction that Auger will not confirm SUGAR
source. (Data may not appear onscreen at low magnification.) Simulations at
http://heseweb.nrl.navy.mil/gamma/~dermer/invest/sim/index.ht
Models and phenomenology
It is evident that models of the knee should match the observational
phenomenology. In this talk I discuss a few aspects of phenomenology, which are
important not only for the understanding of the knee origin, but also for the
general problem of the origin of cosmic rays. Among them are the shape of the
energy spectrum, its irregularity, the sharpness of the knee and its fine
structure. The classification of models is given and some examples of the most
recent models are discussed. The most probable conclusion deduced from this
examination is that the knee has an astrophysical origin and the so called
'source' models of the knee are most likely among them.Comment: 13 pages, 4 figures, overview talk at 19th European Cosmic Ray
Symposium, Firenze, Italy, 30.08-4.09.2004 (to be published in the
Int.J.Mod.Phys.A
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