79,996 research outputs found
CHORIZOS: a CHi-square cOde for parameteRized modelIng and characteriZation of phOtometry and Spectrophotometry
We have developed a CHi-square cOde for parameteRized modelIng and
characteriZation of phOtometry and Spectrophotometry (CHORIZOS). CHORIZOS can
use up to two intrinsic free parameters (e.g. temperature and gravity for
stars; type and redshift for galaxies; or age and metallicity for stellar
clusters) and two extrinsic ones (amount and type of extinction). The code uses
chi-square minimization to find all models compatible with the observed data in
the model N-dimensional (N=1,2,3,4) parameter space. CHORIZOS can use either
correlated or uncorrelated colors as input and is especially designed to
identify possible parameter degeneracies and multiple solutions. The code is
written in IDL and is available to the astronomical community. Here we present
the techniques used, test the code, apply it to a few well-known astronomical
problems, and suggest possible applications. As a first scientific result from
CHORIZOS, we confirm from photometry the need for a revised
temperature-spectral type scale for OB stars previously derived from
spectroscopy.Comment: 32 pages, 13 figures. To appear in the September 2004 issue of PAS
Neutrinoless double-beta decay. A brief review
In this brief review we discuss the generation of Majorana neutrino masses
through the see-saw mechanism, the theory of neutrinoless double-beta decay,
the implications of neutrino oscillation data for the effective Majorana mass,
taking into account the recent Daya Bay measurement of theta_13, and the
interpretation of the results of neutrinoless double-beta decay experiments.Comment: 22 page
Topological phases of fermions in one dimension
In this paper we show how the classification of topological phases in
insulators and superconductors is changed by interactions, in the case of 1D
systems. We focus on the TR-invariant Majorana chain (BDI symmetry class).
While the band classification yields an integer topological index , it is
known that phases characterized by values of in the same equivalence class
modulo 8 can be adiabatically transformed one to another by adding suitable
interaction terms. Here we show that the eight equivalence classes are distinct
and exhaustive, and provide a physical interpretation for the interacting
invariant modulo 8. The different phases realize different Altland-Zirnbauer
classes of the reduced density matrix for an entanglement bipartition into two
half-chains. We generalize these results to the classification of all one
dimensional gapped phases of fermionic systems with possible anti-unitary
symmetries, utilizing the algebraic framework of central extensions. We use
matrix product state methods to prove our results.Comment: 14 pages, 3 figures, v2: references adde
A paradox in bosonic energy computations via semidefinite programming relaxations
We show that the recent hierarchy of semidefinite programming relaxations
based on non-commutative polynomial optimization and reduced density matrix
variational methods exhibits an interesting paradox when applied to the bosonic
case: even though it can be rigorously proven that the hierarchy collapses
after the first step, numerical implementations of higher order steps generate
a sequence of improving lower bounds that converges to the optimal solution. We
analyze this effect and compare it with similar behavior observed in
implementations of semidefinite programming relaxations for commutative
polynomial minimization. We conclude that the method converges due to the
rounding errors occurring during the execution of the numerical program, and
show that convergence is lost as soon as computer precision is incremented. We
support this conclusion by proving that for any element p of a Weyl algebra
which is non-negative in the Schrodinger representation there exists another
element p' arbitrarily close to p that admits a sum of squares decomposition.Comment: 22 pages, 4 figure
Classification of the phases of 1D spin chains with commuting Hamiltonians
We consider the class of spin Hamiltonians on a 1D chain with periodic
boundary conditions that are (i) translational invariant, (ii) commuting and
(iii) scale invariant, where by the latter we mean that the ground state
degeneracy is independent of the system size. We correspond a directed graph to
a Hamiltonian of this form and show that the structure of its ground space can
be read from the cycles of the graph. We show that the ground state degeneracy
is the only parameter that distinguishes the phases of these Hamiltonians. Our
main tool in this paper is the idea of Bravyi and Vyalyi (2005) in using the
representation theory of finite dimensional C^*-algebras to study commuting
Hamiltonians.Comment: 8 pages, improved readability, added exampl
The Landau Distribution for Charged Particles Traversing Thin Films
The Landau distribution as well as its first and second momenta are well
suited for describing the energy loss of charged particles traversing a thin
layer of matter. At present, just rational approximations and asymptotic
expressions for these functions were obtained. In this paper we present a
direct calculation of the integral representation of these functions obtaining
perturbative and nonperturvative solutions expressed in terms of fast
convergent series. We also provide a simple numerical algorithm which allows to
control speed and precision of the results. The testing runs have provided, in
reasonable computing times, correct results up to 13-14 significant digits on
the density and distribution functions and 9-10 on the first and second
momenta. If necessary, this accuracy could be improved by adding more
coefficients to the algorithm.Comment: 29 pages, 4 Table
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