23,144 research outputs found
Rank-finiteness for modular categories
We prove a rank-finiteness conjecture for modular categories: up to
equivalence, there are only finitely many modular categories of any fixed rank.
Our technical advance is a generalization of the Cauchy theorem in group theory
to the context of spherical fusion categories. For a modular category
with , the order of the modular -matrix, the Cauchy
theorem says that the set of primes dividing the global quantum dimension
in the Dedekind domain is identical to that
of .Comment: 25 pages (last version). Version 2: removed weakly integral rank 6
and integral rank 7 section, improved rank 5 classification up to monoidal
equivalence. Version 3: removed rank 5 classification (note title
change)--this will be published separately. Significantly improved expositio
The X-Ray Position and Infrared Counterpart of the Eclipsing X-Ray Pulsar OAO 1657-415
We have measured the precise position of the 38-s eclipsing X-ray pulsar OAO
1657-415 with the Chandra X-Ray Observatory: RA = 17h00m48.90s, Dec =
-41d39m21.6s, equninox J2000, error radius = 0.5 arcsec. Based on the
previously measured pulsar mass function and X-ray eclipse duration, this
10.4-d high-mass X-ray binary is believed to contain a B supergiant companion.
Deep optical imaging of the field did not detect any stars at the Chandra
source position, setting a limit of V>23. However, near-IR imaging revealed a
relatively bright star (J=14.1, H=11.9, K_s=10.7) coincident with the Chandra
position, and we identify this star as the IR counterpart of OAO 1657-415. The
IR colors and magnitudes and the optical non-detections for this star are all
consistent with a highly reddened B supergiant (A_V= 20.4 +/- 1.3) at a
distance of 6.4 +/- 1.5 kpc. This implies an X-ray luminosity of 3e36 erg/s
(2-10 keV). IR spectroscopy can verify the spectral type of the companion and
measure its radial velocity curve, yielding a neutron star mass measurement.Comment: 4 pages. ApJ in press (Vol. 573, July 10 issue
Quantum criticality in a generalized Dicke model
We employ a generalized Dicke model to study theoretically the quantum
criticality of an extended two-level atomic ensemble interacting with a
single-mode quantized light field. Effective Hamiltonians are derived and
diagonalized to investigate numerically their eigenfrequencies for different
quantum phases in the system. Based on the analysis of the eigenfrequencies, an
intriguing quantum-phase transition from a normal phase to a superradiant phase
is revealed clearly, which is quite different from that observed with a
standard Dicke model.Comment: 6 pages, 3 figure
On classification of modular categories by rank
The feasibility of a classification-by-rank program for modular categories
follows from the Rank-Finiteness Theorem. We develop arithmetic, representation
theoretic and algebraic methods for classifying modular categories by rank. As
an application, we determine all possible fusion rules for all rank= modular
categories and describe the corresponding monoidal equivalence classes.Comment: arXiv admin note: substantial text overlap with arXiv:1310.705
Furnishing the Galaxy with Pulsars
The majority of pulsar population synthesis studies performed to date have
focused on isolated pulsar evolution. Those that have incorporated pulsar
evolution within binary systems have tended to either treat binary evolution
poorly of evolve the pulsar population in an ad-hoc manner. Here we present the
first model of the Galactic field pulsar population that includes a
comprehensive treatment of both binary and pulsar evolution. Synthetic
observational surveys mimicking a variety of radio telescopes are then
performed on this population. As such, a complete and direct comparison of
model data with observations of the pulsar population within the Galactic disk
is now possible. The tool used for completing this work is a code comprised of
three components: stellar/binary evolution, Galactic kinematics and survey
selection effects. Here we give a brief overview of the method and assumptions
involved with each component. Some preliminary results are also presented as
well as plans for future applications of the code.Comment: 3 pages, 3 figures, Conference: "40 years of pulsars: Millisecond
pulsars, magnetars and more", McGill University, Montreal, Canada, ed.
A.Cumming et al., AI
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