1,526 research outputs found
L^p boundedness of the wave operator for the one dimensional Schroedinger operator
Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we
consider the associated wave operators W_+, W_- defined as the strong L^2
limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the
wave operators are bounded operators on L^p for all 1<p<\infty, provided
(1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a
resonance. For p=\infty we obtain an estimate in terms of the Hilbert
transform. Some applications to dispersive estimates for equations with
variable rough coefficients are given.Comment: 26 page
Heat Kernel Asymptotics on Homogeneous Bundles
We consider Laplacians acting on sections of homogeneous vector bundles over
symmetric spaces. By using an integral representation of the heat semi-group we
find a formal solution for the heat kernel diagonal that gives a generating
function for the whole sequence of heat invariants. We argue that the obtained
formal solution correctly reproduces the exact heat kernel diagonal after a
suitable regularization and analytical continuation.Comment: 29 pages, Proceedings of the 2007 Midwest Geometry Conference in
Honor of Thomas P. Branso
Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time
We prove that the scattering matrix at a fixed quasi--energy determines
uniquely a time--periodic potential that decays exponentially at infinity. We
consider potentials that for each fixed time belong to in space. The
exponent 3/2 is critical for the singularities of the potential in space. For
this singular class of potentials the result is new even in the
time--independent case, where it was only known for bounded exponentially
decreasing potentials.Comment: In this revised version I give a more detailed motivation of the
class of potentials that I consider and I have corrected some typo
Observational signatures of forming young massive clusters: continuum emission from dense HII regions
Young massive clusters (YMCs) are the most massive star clusters forming in
nearby galaxies and are thought to be a young analogue to the globular
clusters. Understanding the formation process of YMCs leads to looking into
very efficient star formation in high-redshift galaxies suggested by recent
JWST observations. We investigate possible observational signatures of their
formation stage, particularly when the mass of a cluster is increasing via
accretion from a natal molecular cloud. To this end, we study the broad-band
continuum emission from ionized gas and dust enshrouding YMCs, whose formation
is followed by recent radiation-hydrodynamics simulations. We perform
post-process radiative transfer calculations using simulation snapshots and
find characteristic spectral features at radio and far-infrared frequencies. We
show that a striking feature is long-lasting, strong free-free emission from a
10pc-scale HII region with a large emission measure of , corresponding to the mean electron density of
. There is a turnover feature below 10
GHz, a signature of the optically-thick free-free emission, often found in
Galactic ultra-compact HII regions. These features come from the peculiar YMC
formation process, where the cluster's gravity effectively traps photoionized
gas for a long duration and enables continuous star formation within the
cluster. Such large and dense HII regions show distinct distribution on the
density-size diagram, apart from the standard sequence of Galactic HII regions.
This is consistent with the observational trend inferred for extragalactic HII
regions associated with YMCs.Comment: 12 pages, 10 figures, accepted for publication in MNRA
Hidden Order and Dimerization Transition in Chains
We study ground state properties of the quantum antiferromagnetic chain
with a bond alternation H = \sum_{j} [ 1 + \delta (-1)^j ] \mbox{\boldmath
$S$}_{j} \cdot \mbox{\boldmath $S$}_{j+1} by a Quantum Monte Carlo
calculation. We find that the hidden symmetry is broken for
while it is unbroken in the other regions. This confirms
the successive dimerization transitions first predicted by Affleck and Haldane.
Our result shows that these transitions can be understood in terms of the
hidden symmetry breaking, as was discussed using the
Valence-Bond-Solid states. Furthermore, we find that the behavior of the
generalized string correlation is qualitatively very similar to that in the
Valence-Bond-Solid states, including the location of zeroes as a function of
the angle parameter.Comment: 3 pages (LaTex with jpsj-style files
(ftp://ftp.u-tokyo.ac.jp/pub/SOCIETY/JPSJ)) and 1 Postscript figur
On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles
We consider a non relativistic quantum system consisting of heavy and
light particles in dimension three, where each heavy particle interacts with
the light ones via a two-body potential . No interaction is assumed
among particles of the same kind. Choosing an initial state in a product form
and assuming sufficiently small we characterize the asymptotic
dynamics of the system in the limit of small mass ratio, with an explicit
control of the error. In the case K=1 the result is extended to arbitrary
. The proof relies on a perturbative analysis and exploits a
generalized version of the standard dispersive estimates for the
Schr\"{o}dinger group. Exploiting the asymptotic formula, it is also outlined
an application to the problem of the decoherence effect produced on a heavy
particle by the interaction with the light ones.Comment: 38 page
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