5,681 research outputs found
On C*-algebras generated by pairs of q-commuting isometries
We consider the C*-algebras O_2^q and A_2^q generated, respectively, by
isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| <
1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the
relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to
the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that
A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 =
complex conjugate of q_2. In the second part of our paper, we discuss the
complexity of the representation theory of A_2^q. We show that A_2^q is *-wild
for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q
in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies
the relationships between the various deformation systems treate
Stabilization of Polar Nano Regions in Pb-free ferroelectrics
Formation of polar nano regions through solid-solution additions are known to
enhance significantly the functional properties of ferroelectric materials.
Despite considerable progress in characterizing the microscopic behavior of
polar nano regions, understanding their real-space atomic structure and
dynamics of formation remains a considerable challenge. Here, using the method
of dynamic pair distribution function, we provide direct insights into the role
of solid-solution additions towards the stabilization of polar nano regions in
the Pb-free ferroelectric of Ba(Zr,Ti)O3. It is shown that for an optimum level
of substitution of Ti by larger Zr ions, the dynamics of atomic displacements
for ferroelectric polarization are slowed sufficiently, which leads to
increased local correlation among dipoles below THz frequencies. The dynamic
pair distribution function technique demonstrates unique capability to obtain
insights into locally correlated atomic dynamics in disordered materials,
including new Pb-free ferroelectrics, which is necessary to understand and
control their functional properties
Singlet-Triplet Physics and Shell Filling in Carbon Nanotube Double Quantum Dots
An artifcial two-atomic molecule, also called a double quantum dot (DQD), is
an ideal system for exploring few electron physics. Spin-entanglement between
just two electrons can be explored in such systems where singlet and triplet
states are accessible. These two spin-states can be regarded as the two states
in a quantum two-state system, a so-called singlet-triplet qubit. A very
attractive material for realizing spin based qubits is the carbon nanotube
(CNT), because it is expected to have a very long spin coherence time. Here we
show the existence of a gate-tunable singlet-triplet qubit in a CNT DQD. We
show that the CNT DQD has clear shell structures of both four and eight
electrons, with the singlet-triplet qubit present in the four-electron shells.
We furthermore observe inelastic cotunneling via the singlet and triplet
states, which we use to probe the splitting between singlet and triplet, in
good agreement with theory.Comment: Supplement available at:
http://www.fys.ku.dk/~hij/public/singlet-triple_supp.pd
Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized X-ray CT
We study recoverability in fan-beam computed tomography (CT) with sparsity
and total variation priors: how many underdetermined linear measurements
suffice for recovering images of given sparsity? Results from compressed
sensing (CS) establish such conditions for, e.g., random measurements, but not
for CT. Recoverability is typically tested by checking whether a computed
solution recovers the original. This approach cannot guarantee solution
uniqueness and the recoverability decision therefore depends on the
optimization algorithm. We propose new computational methods to test
recoverability by verifying solution uniqueness conditions. Using both
reconstruction and uniqueness testing we empirically study the number of CT
measurements sufficient for recovery on new classes of sparse test images. We
demonstrate an average-case relation between sparsity and sufficient sampling
and observe a sharp phase transition as known from CS, but never established
for CT. In addition to assessing recoverability more reliably, we show that
uniqueness tests are often the faster option.Comment: 18 pages, 7 figures, submitte
Water destruction by X-rays in young stellar objects
We study the H2O chemistry in star-forming environments under the influence
of a central X-ray source and a central far ultraviolet (FUV) radiation field.
The gas-phase water chemistry is modeled as a function of time, hydrogen
density and X-ray flux. To cover a wide range of physical environments,
densities between n_H = 10^4-10^9 cm^-3 and temperatures between T = 10-1000 K
are studied. Three different regimes are found: For T < 100 K, the water
abundance is of order 10^-7-10^-6 and can be somewhat enhanced or reduced due
to X-rays, depending on time and density. For 100 K < T < 250 K, H2O is reduced
from initial x(H2O) ~ 10^-4 following ice evaporation to x(H2O) ~ 10^-6 for F_X
> 10^-3 ergs s-1 cm^-2 (t = 10^4 yrs) and for F_X > 10^-4 ergs s^-1 cm^-2 (t =
10^5 yrs). At higher temperatures (T > 250 K) and hydrogen densities, water can
persist with x(H2O) ~ 10^-4 even for high X-ray fluxes. The X-ray and FUV
models are applied to envelopes around low-mass Class 0 and I young stellar
objects (YSOs). Water is destroyed in both Class 0 and I envelopes on
relatively short timescales (t ~ 5000 yrs) for realistic X-ray fluxes, although
the effect is less prominent in Class 0 envelopes due to the higher X-ray
absorbing densities there. FUV photons from the central source are not
effective in destroying water. The average water abundance in Class I sources
for L_X > 10^27 ergs s^-1 is predicted to be x(H2O) < 10^-6.Comment: 12 pages, 14 figures, Accepted for publication in A&
On boson algebras as Hopf algebras
Certain types of generalized undeformed and deformed boson algebras which
admit a Hopf algebra structure are introduced, together with their Fock-type
representations and their corresponding -matrices. It is also shown that a
class of generalized Heisenberg algebras including those algebras including
those underlying physical models such as that of Calogero-Sutherland, is
isomorphic with one of the types of boson algebra proposed, and can be
formulated as a Hopf algebra.Comment: LaTex, 18 page
Modeling water emission from low-mass protostellar envelopes
Within low-mass star formation, water vapor plays a key role in the chemistry
and energy balance of the circumstellar material. The Herschel Space
Observatory will open up the possibility to observe water lines originating
from a wide range of excitation energies.Our aim is to simulate the emission of
rotational water lines from envelopes characteristic of embedded low-mass
protostars. A large number of parameters that influence the water line emission
are explored: luminosity, density,density slope and water abundances.Both dust
and water emission are modelled using full radiative transfer in spherical
symmetry. The temperature profile is calculated for a given density profile.
The H2O level populations and emission profiles are in turn computed with a
non-LTE line code. The results are analyzed to determine the diagnostic value
of different lines, and are compared with existing observations. Lines can be
categorized in: (i) optically thick lines, including ground-state lines, mostly
sensitive to the cold outer part; (ii) highly excited (E_u>200-250 K) optically
thin lines sensitive to the abundance in the hot inner part; and (iii) lines
which vary from optically thick to thin depending on the abundances. Dust
influences the emission of water significantly by becoming optically thick at
the higher frequencies, and by pumping optically thin lines. A good physical
model of a source, including a correct treatment of dust, is a prerequisite to
infer the water abundance structure and possible jumps at the evaporation
temperature from observations. The inner warm (T>100 K) envelope can be probed
byhighly-excited lines, while a combination of excited and spectrally resolved
ground state lines probes the outer envelope. Observations of H218O lines,
although weak, provide even stronger constraints on abundances.Comment: 17 pages with an online appendix of 6 pages. Accepted by A&A. Several
figures are too large for astro-ph. These can be downloaded from
http://www.strw.leidenuniv.nl/~kempen/water.ph
Physical and chemical fingerprint of protostellar disc formation
(Abridged) The purpose of this paper is to explore and compare the physical
and chemical structure of Class I low-mass protostellar sources on
protoplanetary disc scales. We present a study of the dust and gas emission
towards a representative sample of 12 Class I protostars from the Ophiuchus
molecular cloud with the Atacama Large Millimeter/submillimeter Array (ALMA).
The continuum at 0.87 mm and molecular transitions from C17O, C34S, H13CO+,
CH3OH, SO2 , and C2H were observed at high angular resolution (0.4", ~60 au
diameter) towards each source. Disc and stellar masses are estimated from the
continuum flux and position-velocity diagrams, and six of the sources show
disc-like structures. Towards the more luminous sources, compact emission and
large line widths are seen for transitions of SO2 that probe warm gas (Eu ~200
K). In contrast, C17O emission is detected towards the least evolved and less
luminous systems. No emission of CH3OH is detected towards any of the continuum
peaks, indicating an absence of warm CH3OH gas towards these sources. A
power-law relation is seen between the stellar mass and the bolometric
luminosity, corresponding to a mass accretion rate of (2.4 +/- 0.6) x 10^-7
Msun/year for the Class I sources. This mass accretion rate is lower than the
expected value if the accretion is constant in time and rather points to a
scenario of accretion occurring in bursts. The differentiation between C17O and
SO2 suggests that they trace different physical components: C17O traces the
densest and colder regions of the disc-envelope system, while SO2 may be
associated with regions of higher temperature, such as accretion shocks. The
lack of warm CH3OH emission suggests that there is no hot-core-like region
around any of the sources and that the CH3OH column density averaged over the
disc is low.Comment: 20 pages, 16 figures, 8 table
Water in low-mass star-forming regions with Herschel: HIFI spectroscopy of NGC1333
'Water In Star-forming regions with Herschel' (WISH) is a key programme
dedicated to studying the role of water and related species during the
star-formation process and constraining the physical and chemical properties of
young stellar objects. The Heterodyne Instrument for the Far-Infrared (HIFI) on
the Herschel Space Observatory observed three deeply embedded protostars in the
low-mass star-forming region NGC1333 in several H2-16O, H2-18O, and CO
transitions. Line profiles are resolved for five H16O transitions in each
source, revealing them to be surprisingly complex. The line profiles are
decomposed into broad (>20 km/s), medium-broad (~5-10 km/s), and narrow (<5
km/s) components. The H2-18O emission is only detected in broad 1_10-1_01 lines
(>20 km/s), indicating that its physical origin is the same as for the broad
H2-16O component. In one of the sources, IRAS4A, an inverse P Cygni profile is
observed, a clear sign of infall in the envelope. From the line profiles alone,
it is clear that the bulk of emission arises from shocks, both on small (<1000
AU) and large scales along the outflow cavity walls (~10 000 AU). The H2O line
profiles are compared to CO line profiles to constrain the H2O abundance as a
function of velocity within these shocked regions. The H2O/CO abundance ratios
are measured to be in the range of ~0.1-1, corresponding to H2O abundances of
~10-5-10-4 with respect to H2. Approximately 5-10% of the gas is hot enough for
all oxygen to be driven into water in warm post-shock gas, mostly at high
velocities.Comment: Accepted for publication in the A&A HIFI special issu
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