1,886 research outputs found
A reason for fusion rules to be even
We show that certain tensor product multiplicities in semisimple braided
sovereign tensor categories must be even. The quantity governing this behavior
is the Frobenius-Schur indicator. The result applies in particular to the
representation categories of large classes of groups, Lie algebras, Hopf
algebras and vertex algebras.Comment: 6 pages, LaTe
A discontinuity in the low-mass initial mass function
The origin of brown dwarfs (BDs) is still an unsolved mystery. While the
standard model describes the formation of BDs and stars in a similar way recent
data on the multiplicity properties of stars and BDs show them to have
different binary distribution functions. Here we show that proper treatment of
these uncovers a discontinuity of the multiplicity-corrected mass distribution
in the very-low-mass star (VLMS) and BD mass regime. A continuous IMF can be
discarded with extremely high confidence. This suggests that VLMSs and BDs on
the one hand, and stars on the other, are two correlated but disjoint
populations with different dynamical histories. The analysis presented here
suggests that about one BD forms per five stars and that the BD-star binary
fraction is about 2%-3% among stellar systems.Comment: 14 pages, 11 figures, uses emulateapj.cls. Minor corrections and 1
reference added after being accepted by the Ap
Diffusion-limited reactions on disordered surfaces with continuous distributions of binding energies
We study the steady state of a stochastic particle system on a
two-dimensional lattice, with particle influx, diffusion and desorption, and
the formation of a dimer when particles meet. Surface processes are thermally
activated, with (quenched) binding energies drawn from a \emph{continuous}
distribution. We show that sites in this model provide either coverage or
mobility, depending on their energy. We use this to analytically map the system
to an effective \emph{binary} model in a temperature-dependent way. The
behavior of the effective model is well-understood and accurately describes key
quantities of the system: Compared with discrete distributions, the temperature
window of efficient reaction is broadened, and the efficiency decays more
slowly at its ends. The mapping also explains in what parameter regimes the
system exhibits realization dependence.Comment: 23 pages, 8 figures. Submitted to: Journal of Statistical Mechanics:
Theory and Experimen
Correlated radio--X-ray variability of Galactic Black Holes: A radio--X-ray flare in Cygnus X-1
We report on the first detection of a quasi-simultaneous radio-X-ray flare of
Cygnus X-1. The detection was made on 2005 April 16 with pointed observations
by the Rossi X-ray Timing Explorer and the Ryle telescope, during a phase where
the black hole candidate was close to a transition from the its soft into its
hard state. The radio flare lagged the X-rays by approximately 7 minutes,
peaking at 3:20 hours barycentric time (TDB 2453476.63864). We discuss this lag
in the context of models explaining such flaring events as the ejection of
electron bubbles emitting synchrotron radiation.Comment: 4 pages, 4 figure
Stellar Bar Evolution in Cuspy and Flat-Cored Triaxial CDM Halos
We analyze the evolution of stellar bars in galactic disks in mildly triaxial
flat-core and cuspy CDM halos. We use tailored simulations of rigid and live
halos which include the feedback from disk/bar onto the halo in order to test
the work by El-Zant & Shlosman (2002). The latter used the Liapunov exponents
to analyze the fate of bars in analytical asymmetric halos. We find: (1) The
bar growth is similar in all rigid axisymmetric and triaxial halos. (2) Bars in
live models vertically buckle and form a pseudobulge with a boxy/peanut shape.
(3) In live axisymmetric halos, the bar strength varies little during the
secular evolution. The bar pattern speed anticorrelates with the halo core
size. The bar strength is larger for smaller disk-to-halo mass ratios within
disk radii, the bar size correlates with the halo core sizes, and the bar
pattern speeds -- with the halo central mass concentration. Bars embedded in
live triaxial halos have a starkly different fate: they dissolve on ~1.5-5 Gyr
due to the onset of chaos over continuous zones, leaving behind a weak oval
distortion. The onset of chaos is related to the halo triaxiality, the fast
rotating bar and the halo cuspiness. Before the bar dissolves, the region
outside it develops strong spiral structures, especially in the live triaxial
halos. (4) More angular momentum is absorbed by the triaxial halos as compared
to the axisymmetric models and its exchange is mediated by resonances. (5)
Cuspy halos are more susceptible than flat-core halos to having their
prolateness washed out by the bar. We analyze these results in terms of the
stability of trajectories and development of chaos. We set constraints on the
triaxiality of DM halos by comparing our predictions to recent observations of
bars out to z~1.Comment: 17 pages, 14 figures, Astrophysical Journal, in press, Vol. 637.
Updated version (text, references
Exactly solvable statistical model for two-way traffic
We generalize a recently introduced traffic model, where the statistical
weights are associated with whole trajectories, to the case of two-way flow. An
interaction between the two lanes is included which describes a slowing down
when two cars meet. This leads to two coupled five-vertex models. It is shown
that this problem can be solved by reducing it to two one-lane problems with
modified parameters. In contrast to stochastic models, jamming appears only for
very strong interaction between the lanes.Comment: 6 pages Latex, submitted to J Phys.
Calculation of reduced density matrices from correlation functions
It is shown that for solvable fermionic and bosonic lattice systems, the
reduced density matrices can be determined from the properties of the
correlation functions. This provides the simplest way to these quantities which
are used in the density-matrix renormalization group method.Comment: 4 page
Density Matrices for a Chain of Oscillators
We consider chains with an optical phonon spectrum and study the reduced
density matrices which occur in density-matrix renormalization group (DMRG)
calculations. Both for one site and for half of the chain, these are found to
be exponentials of bosonic operators. Their spectra, which are correspondingly
exponential, are determined and discussed. The results for large systems are
obtained from the relation to a two-dimensional Gaussian model.Comment: 15 pages,8 figure
Symmetry breaking and phase coexistence in a driven diffusive two-channel system
We consider classical hard-core particles moving on two parallel chains in
the same direction. An interaction between the channels is included via the
hopping rates. For a ring, the stationary state has a product form. For the
case of coupling to two reservoirs, it is investigated analytically and
numerically. In addition to the known one-channel phases, two new regions are
found, in particular the one, where the total density is fixed, but the filling
of the individual chains changes back and forth, with a preference for strongly
different densities. The corresponding probability distribution is determined
and shown to have an universal form. The phase diagram and general aspects of
the problem are discussed.Comment: 12 pages, 10 figures, to appear in Phys.Rev.
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