68,532 research outputs found
Kernel functions and B\"acklund transformations for relativistic Calogero-Moser and Toda systems
We obtain kernel functions associated with the quantum relativistic Toda
systems, both for the periodic version and for the nonperiodic version with its
dual. This involves taking limits of previously known results concerning kernel
functions for the elliptic and hyperbolic relativistic Calogero-Moser systems.
We show that the special kernel functions at issue admit a limit that yields
generating functions of B\"acklund transformations for the classical
relativistic Calogero-Moser and Toda systems. We also obtain the
nonrelativistic counterparts of our results, which tie in with previous results
in the literature.Comment: 76 page
Effect of the Milky Way on Magellanic Cloud structure
A combination of analytic models and n-body simulations implies that the
structural evolution of the Large Magellanic Cloud (LMC) is dominated by its
dynamical interaction with the Milky Way. Although expected at some level, the
scope of the involvement has significant observational consequences. First, LMC
disk orbits are torqued out of the disk plane, thickening the disk and
populating a spheroid. The torque results from direct forcing by the Milky Way
tide and, indirectly, from the drag between the LMC disk and its halo resulting
from the induced precession of the LMC disk. The latter is a newly reported
mechanism that can affect all satellite interations. However, the overall
torque can not isotropize the stellar orbits and their kinematics remains
disk-like. Such a kinematic signature is observed for nearly all LMC
populations. The extended disk distribution is predicted to increase the
microlensing toward the LMC. Second, the disk's binding energy slowly decreases
during this process, puffing up and priming the outer regions for subsequent
tidal stripping. Because the tidally stripped debris will be spatially
extended, the distribution of stripped stars is much more extended than the HI
Magellanic Stream. This is consistent with upper limits to stellar densities in
the gas stream and suggests a different strategy for detecting the stripped
stars. And, finally, the mass loss over several LMC orbits is predicted by
n-body simulation and the debris extends to tens of kiloparsecs from the tidal
boundary. Although the overall space density of the stripped stars is low,
possible existence of such intervening populations have been recently reported
and may be detectable using 2MASS.Comment: 15 pages, color Postscript figures, uses emulateapj.sty. Also
available from http://www-astro.phast.umass.edu/~weinberg/weinberg-pubs.htm
Dark Matter: Introduction
This short review was prepared as an introduction to the Royal Society's
'Dark Matter' conference. It addresses the embarrassing fact that 95% of the
universe is unaccounted for. Favoured dark matter candidates are axions or
weakly-interacting particles that have survived from the very early universe,
but more exotic options cannot be excluded. Experimental searches are being
made for the 'dark' particles but we have indirect clues to their nature too.
Comparisons of data (from, eg, gravitational lensing) with numerical
simulations of galaxy formation can constrain (eg) the particle velocities and
collision cross sections.
The mean cosmic density of dark matter (plus baryons) is now pinned down to
be only about 30% of the critical density However, other recent evidence --
microwave background anisotropies, complemented by data on distant supernovae
-- reveals that our universe actually is 'flat', and that its dominant
ingredient (about 70% of the total mass-energy) is something quite unexpected
-- 'dark energy' pervading all space, with negative pressure. We now confront
two mysteries:
(i) Why does the universe have three quite distinct basic ingredients --
baryons, dark matter and dark energy -- in the proportions (roughly) 5%, 25%
and 70%?
(ii) What are the (almost certainly profound) implications of the 'dark
energy' for fundamental physics?Comment: 10 pages, 1 figure. Late
Crossing Symmetry Violation of Unitarized Pion-Pion Amplitude in the Resonance Region
Pion-pion scattering amplitude obtained from one-loop Chiral Perturbation
Theory (ChPT) is crossing symmetric, however the corresponding partial wave
amplitudes do not respect exact unitarity relation. There are different
approaches to get unitarized partial wave amplitudes from ChPT. Here we
consider the inverse amplitude method (IAM) that is often used to fit pion-pion
phase shifts to experimental data, by adjusting free parameters. We measure the
amount of crossing symmetry violation (CSV) in this case and we show that
crossing symmetry is badly violated by the IAM unitarized ChPT amplitude in the
resonance region. Important CSV also occurs when all free parameters are set
equal to zero.Comment: 6 pages, 4 figure
Parametric instability in dark molecular clouds
The present work investigates the parametric instability of parallel
propagating circularly polarized Alfven(pump) waves in a weakly ionized
molecular cloud. It is shown that the relative drift between the plasma
particles gives rise to the Hall effect resulting in the modified pump wave
characteristics. Although the linearized fluid equations with periodic
coefficients are difficult to solve analytically, it is shown that a linear
transformation can remove the periodic dependence. The resulting linearized
equations with constant coefficients are used to derive an algebraic dispersion
relation. The growth rate of the parametric instability is a sensitive function
of the amplitude of the pump wave as well as to the ratio of the pump and the
modified dust-cyclotron frequencies. The instability is insensitive to the
plasma-beta The results are applied to the molecular clouds.Comment: 27 page, 5 figures, accepted in Ap
Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions
We calculate the partition function of the -state Potts model
exactly for strips of the square and triangular lattices of various widths
and arbitrarily great lengths , with a variety of boundary
conditions, and with and restricted to satisfy conditions corresponding
to the ferromagnetic phase transition on the associated two-dimensional
lattices. From these calculations, in the limit , we determine
the continuous accumulation loci of the partition function zeros in
the and planes. Strips of the honeycomb lattice are also considered. We
discuss some general features of these loci.Comment: 12 pages, 12 figure
Ground-state energy and depletions for a dilute binary Bose gas
When calculating the ground-state energy of a weakly interacting Bose gas
with the help of the customary contact pseudopotential, one meets an artifical
ultraviolet divergence which is caused by the incorrect treatment of the true
interparticle interactions at small distances. We argue that this problem can
be avoided by retaining the actual, momentum-dependent interaction matrix
elements, and use this insight for computing both the ground-state energy and
the depletions of a binary Bose gas mixture. Even when considering the
experimentally relevant case of equal masses of both species, the resulting
expressions are quite involved, and no straightforward generalizations of the
known single-species formulas. On the other hand, we demonstrate in detail how
these latter formulas are recovered from our two-species results in the limit
of vanishing interspecies interaction.Comment: 11 pages, Phys. Rev. A in pres
Jet Investigations Using the Radial Moment
We define the radial moment, , for jets produced in hadron-hadron
collisions. It can be used as a tool for studying, as a function of the jet
transverse energy and pseudorapidity, radiation within the jet and the quality
of a perturbative description of the jet shape. We also discuss how
non-perturbative corrections to the jet transverse energy affect .Comment: 14 pages, LaTeX, 6 figure
Analytical solution of the optimal laser control problem in two-level systems
The optimal control of two-level systems by time-dependent laser fields is
studied using a variational theory. We obtain, for the first time, general
analytical expressions for the optimal pulse shapes leading to global
maximization or minimization of different physical quantities. We present
solutions which reproduce and improve previous numerical results.Comment: 12 pages, 2 figure
Accretion-Induced Lithium Line Enhancements in Classical T Tauri Stars: RW Aur
It is widely accepted that much of the stochastic variability of T Tauri
stars is due to accretion by a circumstellar disk. The emission line spectrum
as well as the excess continuum emission are common probes of this process. In
this communication, we present additional probes of the circumstellar
environment in the form of resonance lines of low ionization potential
elements. Using a set of 14 high resolution echelle observations of the
classical T Tauri star (CTTS), RW Aur, taken between 1986 and 1996, we
carefully measure the continuum veiling at each epoch by comparing more than
500 absorption lines with those of an appropriate template. This allows us to
accurately subtract out the continuum emission and to recover the underlying
photospheric spectrum. In doing so, we find that selected photospheric lines
are enhanced by the accretion process, namely the resonance lines of LiI and
KI. A resonance line of TiI and a low excitation potential line of CaI also
show weak enhancements. Simple slab models and computed line bisectors lead us
to propose that these line enhancements are markers of cool gas at the
beginning of the accretion flow which provides an additional source of line
opacity. These results suggest that published values of surface lithium
abundances of classical T Tauri stars are likely to be overestimated. This
would account for the various reports of surface lithium abundances in excess
of meteoritic values among the extreme CTTS. Computing LTE lithium abundances
of RW Aur in a low and then high accretion state yields abundances which vary
by one order of magnitude. The low accretion state lithium abundance is
consistent with theoretical predictions for a star of this age and mass while
the high accretion state spectrum yields a super-meteoritic lithium abundance.Comment: 28 pages, 8 figures, accepted by Ap
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