1,696 research outputs found
Extremely High Energy Neutrinos and their Detection
We discuss in some detail the production of extremely high energy (EHE)
neutrinos with energies above 10^18 eV. The most certain process for producing
such neutrinos results from photopion production by EHE cosmic rays in the
cosmic background photon field. However, using assumptions for the EHE cosmic
ray source evolution which are consistent with results from the deep QSO survey
in the radio and X-ray range, the resultant flux of neutrinos from this process
is not strong enough for plausible detection. A measurable flux of EHE
neutrinos may be present, however, if the highest energy cosmic rays which have
recently been detected well beyond 10^20 eV are the result of the annihilation
of topological defects which formed in the early universe. Neutrinos resulting
from such decays reach energies of the grand unification (GUT) scale, and
collisions of superhigh energy neutrinos with the cosmic background neutrinos
initiate neutrino cascading which enhances the EHE neutrino flux at Earth. We
have calculated the neutrino flux including this cascading effect for either
massless or massive neutrinos and we find that these fluxes are conceivably
detectable by air fluorescence detectors now in development. The
neutrino-induced showers would be recognized by their starting deep in the
atmosphere. We evaluate the feasibility of detecting EHE neutrinos this way
using air fluorescence air shower detectors and derive the expected event rate.
Other processes for producing deeply penetrating air showers constitute a
negligible background.Comment: 33 pages, including 12 eps figures, LaTe
On Equilibrium Dynamics of Spin-Glass Systems
We present a critical analysis of the Sompolinsky theory of equilibrium
dynamics. By using the spherical spin glass model we test the asymptotic
static limit of the Sompolinsky solution showing that it fails to yield a
thermodynamically stable solution. We then present an alternative formulation,
based on the Crisanti, H\"orner and Sommers [Z. f\"ur Physik {\bf 92}, 257
(1993)] dynamical solution of the spherical -spin spin glass model,
reproducing a stable static limit that coincides, in the case of a one step
Replica Symmetry Breaking Ansatz, with the solution at the dynamic free energy
threshold at which the relaxing system gets stuck off-equilibrium. We formally
extend our analysis to any number of Replica Symmetry Breakings . In the
limit both formulations lead to the Parisi anti-parabolic
differential equation. This is the special case, though, where no dynamic
blocking threshold occurs. The new formulation does not contain the additional
order parameter of the Sompolinsky theory.Comment: 24 pages, 6 figure
The spherical spin glass model: an exactly solvable model for glass to spin-glass transition
We present the full phase diagram of the spherical spin glass model
with . The main outcome is the presence of a new phase with both
properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models,
e.g, the Sherrington-Kirkpatrick model, and those of One Replica Symmetry
Breaking (1RSB). The phase, which separates a 1RSB phase from FRSB phase, is
described by an order parameter function with a continuous part (FRSB)
for and a discontinuous jump (1RSB) at . This phase has a finite
complexity which leads to different dynamic and static properties.Comment: 5 pages, 2 figure
Thermodynamic Properties and Phase Transitions in a Mean-Field Ising Spin Glass on Lattice Gas: the Random Blume-Emery-Griffiths-Capel Model
The study of the mean-field static solution of the Random
Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched
random magnetic interaction, is performed. The model exhibits a paramagnetic
phase, described by a stable Replica Symmetric solution. When the temperature
is decreased or the density increases, the system undergoes a phase transition
to a Full Replica Symmetry Breaking spin-glass phase. The nature of the
transition can be either of the second order (like in the
Sherrington-Kirkpatrick model) or, at temperature below a given critical value,
of the first order in the Ehrenfest sense, with a discontinuous jump of the
order parameter and accompanied by a latent heat. In this last case coexistence
of phases takes place. The thermodynamics is worked out in the Full Replica
Symmetry Breaking scheme, and the relative Parisi equations are solved using a
pseudo-spectral method down to zero temperature.Comment: 24 pages, 12 figure
Entanglement of random vectors
We analytically calculate the average value of i-th largest Schmidt
coefficient for random pure quantum states. Schmidt coefficients, i.e.,
eigenvalues of the reduced density matrix, are expressed in the limit of large
Hilbert space size and for arbitrary bipartite splitting as an implicit
function of index i.Comment: 8 page
Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices
We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the SOP and for their Cauchy transforms, given as expectation values of traces and determinants or their inverses, respectively. Our proof uses the fact that the joint probability distribution function for all combinations of real eigenvalues and complex conjugate eigenvalue pairs can be written as a product. Examples for the SOP are given in terms of Laguerre polynomials for the chiral ensemble (also called the non-Hermitian real Wishart-Laguerre ensemble), both without and with the insertion of characteristic polynomials. Such characteristic polynomials play the role of mass terms in applications to complex Dirac spectra in field theory. In addition, for the elliptic real Ginibre ensemble we recover the SOP of Forrester and Nagao in terms of Hermite polynomials
Schur function averages for the real Ginibre ensemble
We derive an explicit simple formula for expectations of all Schur functions
in the real Ginibre ensemble. It is a positive integer for all entries of the
partition even and zero otherwise. The result can be used to determine the
average of any analytic series of elementary symmetric functions by Schur
function expansion
Statistical properties of random density matrices
Statistical properties of ensembles of random density matrices are
investigated. We compute traces and von Neumann entropies averaged over
ensembles of random density matrices distributed according to the Bures
measure. The eigenvalues of the random density matrices are analyzed: we derive
the eigenvalue distribution for the Bures ensemble which is shown to be broader
then the quarter--circle distribution characteristic of the Hilbert--Schmidt
ensemble. For measures induced by partial tracing over the environment we
compute exactly the two-point eigenvalue correlation function.Comment: 8 revtex pages with one eps file included, ver. 2 - minor misprints
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