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 $R$-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