15,820 research outputs found
Line lists for the A2PI-X2Sigma+ (red) and {B2Sigma+-X2Sigma} (violet) Systems of CN, 13C14N, and 12C15N, and Application to Astronomical Spectra
New red and violet system line lists for the CN isotopologues 13C14N and
12C15N have been generated. These new transition data are combined with those
previously derived for 12C14N, and applied to the determination of CNO
abundances in the solar photosphere and in four red giant stars: Arcturus, the
bright very low-metallicity star HD 122563, and carbon-enhanced metal-poor
stars HD 196944 and HD 201626. When lines of both red and violet system lines
are detectable in a star, their derived N abundances are in good agreement. The
mean N abundances determined in this work generally are also in accord with
published values.Comment: ApJS, in press, 37 pages, 7 figures, 3 table
Proof of a universal lower bound on the shear viscosity to entropy density ratio
It has been conjectured, on the basis of the gauge-gravity duality, that the
ratio of the shear viscosity to the entropy density should be universally
bounded from below by 1/ 4 pi in units of the Planck constant divided by the
Boltzmann constant. Here, we prove the bound for any ghost-free extension of
Einstein gravity and the field-theory dual thereof. Our proof is based on the
fact that, for such an extension, any gravitational coupling can only increase
from its Einstein value. Therefore, since the shear viscosity is a particular
gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show
that the entropy density can always be calibrated to its Einstein value. Our
general principles are demonstrated for a pair of specific models, one with
ghosts and one without.Comment: 14 page
Phases of information release during black hole evaporation
In a recent article, we have shown how quantum fluctuations of the background
geometry modify Hawking's density matrix for black hole (BH) radiation.
Hawking's diagonal matrix picks up small off-diagonal elements whose influence
becomes larger with the number of emitted particles. We have calculated the
"time-of-first-bit", when the first bit of information comes out of the BH, and
the "transparency time", when the rate of information release becomes order
unity. We have found that the transparency time is equal to the "Page time",
when the BH has lost half of its initial entropy to the radiation, in agreement
with Page's results. Here, we improve our previous calculation by keeping track
of the time of emission of the Hawking particles and their back-reaction on the
BH. Our analysis reveals a new time scale, the radiation "coherence time",
which is equal to the geometric mean of the evaporation time and the light
crossing time. We find, as for our previous treatment, that the
time-of-first-bit is equal to the coherence time, which is much shorter than
the Page time. But the transparency time is now much later than the Page time,
just one coherence time before the end of evaporation. Close to the end, when
the BH is parametrically of Planckian dimensions but still large, the coherence
time becomes parametrically equal to the evaporation time, thus allowing the
radiation to purify. We also determine the time dependence of the entanglement
entropy of the early and late-emitted radiation. This entropy is small during
most of the lifetime of the BH, but our qualitative analysis suggests that it
becomes parametrically maximal near the end of evaporation.Comment: 51 pages, 1 figur
Commuting families in Hecke and Temperley-Lieb algebras
Abstract
We define analogs of the Jucys-Murphy elements for the affine Temperley-Lieb algebra and give their explicit expansion in terms of the basis of planar Brauer diagrams. These Jucys-Murphy elements are a family of commuting elements in the affine Temperley-Lieb algebra, and we compute their eigenvalues on the generic irreducible representations. We show that they come from Jucys-Murphy elements in the affine Hecke algebra of type A, which in turn come from the Casimir element of the quantum group . We also give the explicit specializations of these results to the finite Temperley-Lieb algebra.12
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