8,311 research outputs found
The energy spectrum observed by the AGASA experiment and the spatial distribution of the sources of ultra-high energy cosmic rays
Seven and a half years of continuous monitoring of giant air showers
triggered by ultra high-energy cosmic rays have been recently summarized by the
AGASA collaboration. The resulting energy spectrum indicates clearly that the
cosmic ray spectrum extends well beyond the Greisen-Zatsepin-Kuzmin (GZK)
cut-off at eV. Furthermore, despite the small number
statistics involved, some structure in the spectrum may be emerging. Using
numerical simulations, it is demonstrated in the present work that these
features are consistent with a spatial distribution of sources that follows the
distribution of luminous matter in the local Universe. Therefore, from this
point of view, there is no need for a second high-energy component of cosmic
rays dominating the spectrum beyond the GZK cut-off.Comment: 14 pages, 4 figures, Astrophys. J. Letters (submitted
On the significance of the observed clustering of ultra-high energy cosmic rays
Three pairs of possibly correlated ultra-high energy cosmic ray events were
reported by Hayashida et al (1996). Here we calculate the propagation of the
corresponding particles through both the intergalactic and galactic magnetic
fields. The large scale disc and halo magnetic components are approximated by
the models of Stanev (1997). The intergalactic magnetic field intensity is
modulated by the actual density of luminous matter along the corresponding
lines of sight, calculated from the CfA redshift catalogue (Huchra et al,
1995). The results indicate that, if the events of each pair had a common
source and were simultaneously produced, they either originated inside the
galactic halo or otherwise very unlikely events were observed. On the other
hand, an estimate of the arrival probability of ultra-high energy cosmic rays,
under the assumption that the distribution of luminous matter in the nearby
universe traces the distribution of the sources of the particles and intensity
of the intergalactic magnetic field, suggests that the pairs are chance
clusterings.Comment: Ap. J. Letters Accepted - 13 pages + 4 figure
Acceptance of fluorescence detectors and its implication in energy spectrum inference at the highest energies
Along the years HiRes and AGASA experiments have explored the fluorescence
and the ground array experimental techniques to measure extensive air showers,
being both essential to investigate the ultra-high energy cosmic rays. However,
such Collaborations have published contradictory energy spectra for energies
above the GZK cut-off. In this article, we investigate the acceptance of
fluorescence telescopes to different primary particles at the highest energies.
Using CORSIKA and CONEX shower simulations without and with the new
pre-showering scheme, which allows photons to interact in the Earth magnetic
field, we estimate the aperture of the HiRes-I telescope for gammas, iron
nuclei and protons primaries as a function of the number of simulated events
and primary energy. We also investigate the possibility that systematic
differences in shower development for hadrons and gammas could mask or distort
vital features of the cosmic ray energy spectrum at energies above the
photo-pion production threshold. The impact of these effects on the true
acceptance of a fluorescence detector is analyzed in the context of top-down
production models
Spin superfluidity and spin-orbit gauge symmetry fixing
The Hamiltonian describing 2D electron gas, in a spin-orbit active medium,
can be cast into a consistent non-Abelian gauge field theory leading to a
proper definition of the spin current. The generally advocated gauge symmetric
version of the theory results in current densities that are gauge covariant, a
fact that poses severe concerns on their physical nature. We show that in fact
the problem demands gauge fixing, leaving no room to ambiguity in the
definition of physical spin currents. Gauge fixing also allows for polarized
edge excitations not present in the gauge symmetric case. The scenario here is
analogous to that of superconductivity gauge theory. We develop a variational
formulation that accounts for the constraints between U(1) physical fields and
SU(2) gauge fields and show that gauge fixing renders a physical matter and
radiation currents and derive the particular consequences for the Rashba SO
interaction.Comment: to appear in EP
Directed paths on hierarchical lattices with random sign weights
We study sums of directed paths on a hierarchical lattice where each bond has
either a positive or negative sign with a probability . Such path sums
have been used to model interference effects by hopping electrons in the
strongly localized regime. The advantage of hierarchical lattices is that they
include path crossings, ignored by mean field approaches, while still
permitting analytical treatment. Here, we perform a scaling analysis of the
controversial ``sign transition'' using Monte Carlo sampling, and conclude that
the transition exists and is second order. Furthermore, we make use of exact
moment recursion relations to find that the moments always determine,
uniquely, the probability distribution $P(J)$. We also derive, exactly, the
moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations
($n\to 0$) to obtain for odd and even moments yield a new signal for
the transition that coincides with Monte Carlo simulations. Analysis of high
moments yield interesting ``solitonic'' structures that propagate as a function
of . Finally, we derive the exact probability distribution for path sums
up to length L=64 for all sign probabilities.Comment: 20 pages, 12 figure
A Unified Algebraic Approach to Classical Yang-Baxter Equation
In this paper, the different operator forms of classical Yang-Baxter equation
are given in the tensor expression through a unified algebraic method. It is
closely related to left-symmetric algebras which play an important role in many
fields in mathematics and mathematical physics. By studying the relations
between left-symmetric algebras and classical Yang-Baxter equation, we can
construct left-symmetric algebras from certain classical r-matrices and
conversely, there is a natural classical r-matrix constructed from a
left-symmetric algebra which corresponds to a parak\"ahler structure in
geometry. Moreover, the former in a special case gives an algebraic
interpretation of the ``left-symmetry'' as a Lie bracket ``left-twisted'' by a
classical r-matrix.Comment: To appear in Journal of Physics A: Mathematical and Theoretica
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Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance
We study quantum interference effects on the transition strength for strongly
localized electrons hopping on 2D square and 3D cubic lattices in a magnetic
field B. In 2D, we obtain closed-form expressions for the tunneling probability
between two arbitrary sites by exactly summing the corresponding phase factors
of all directed paths connecting them. An analytic expression for the
magnetoconductance, as an explicit function of the magnetic flux, is derived.
In the experimentally important 3D case, we show how the interference patterns
and the small-B behavior of the magnetoconductance vary according to the
orientation of B.Comment: 4 pages, RevTe
On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized
On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized
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