Weyl law for fat fractals

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.Comment: 8 pages, 4 figures, IOP forma

Shocks and PDRs in an intermediate mass star forming globule: the case of IC1396N

The dark globule IC1396N is a typical example of a star formation process induced by radiation driven implosion due to the strong UV field from a nearby O6 star. The IRAS source embedded in the globule and its associated molecular outflow have been observed with the Long Wavelength Spectrometer (LWS) on ISO revealing an extremely rich spectrum including: CO rotational lines from J=14-13 up to J=28-27, rotational lines from ortho-H2O, OH lines involving the first four rotational levels of both ladders, atomic (OI 63μm, OI 145μm) and ionic (CII 157μm, OIII 52μm, OIII 88μm) lines. A complex picture arises, where an externally illuminated PDR coexists with strong C-shocks within IC1396N and whose origin is not clear

High-J CO line emission from young stellar objects: from ISO to FIRST

we present the CO pure rotational spectrum at high J (Jup14) obtained with the Long Wavelength Spectrometer (LWS) on board of the ISO satellite towards molecular outflows exciting sources in nearby star formation regions. The physical conditions, derived using an LVG model for the line emission, indicate the presence of warm and dense gas, probably shock excited. The model fits show that often the bulk of this CO emission is expected in the spectral range that will be covered by FIRST, indicating the potentiality of this satellite to trace the warm component of gas emission in young stellar objects

Semiclassical structure of chaotic resonance eigenfunctions

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the non-unitary quantum propagator, and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as $\hbar\to 0$ on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates $\{\psi(\hbar)\}_{\hbar\to 0}$ is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker map, for which the probability density in position space is observed to have self-similarity properties.Comment: 4 pages, 4 figures; some minor corrections, some changes in presentatio

Urticaria associated with hyper-IgE in a patient with psoriasis undergoing treatment with efalizumab.

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Irreversible Quantum Baker Map

We propose a generalization of the model of classical baker map on the torus, in which the images of two parts of the phase space do overlap. This transformation is irreversible and cannot be quantized by means of a unitary Floquet operator. A corresponding quantum system is constructed as a completely positive map acting in the space of density matrices. We investigate spectral properties of this super-operator and their link with the increase of the entropy of initially pure states.Comment: 4 pages, 3 figures include

ISO-LWS observations of IRAS16293-2422

We obtained LWS grating spectra toward IRAS 16293-2422 and the surrounding region, which covers the entire extent of the molecular outflow. The LWS spectra show that the region is relatively uncontaminated by PhotoDissociationRegion (PDR)-like emission, showing only a weak diffuse CII emission. The on-source spectrum revealed the presence of the OI(63μm) line and several lines from CO, H2O and OH molecules. In this work we derive the macroscopic quantities associated with the UV-illuminated emitting gas which surrounds IRAS16293-2422 and compare it with previous studies. We show that the molecular lines originate in a hot (~1600 K), dense (~ 3·104cm-3) and extended (~ 8·1016cm) region, that we interprete as the shock of the wind impacting obliquely with the walls of the cavity created by the wind itself. The OI(63μm) line observed by the Kuiper Airborne Observatory (KAO: Ceccarelli et al. 1997a) at ~ 1.2·1017cm west from the central source is hence interpreted as the head of the shock where the wind strikes the ambient gas. Finally we speculate that the OI(63μm) line emission seen on-source originates in the collapsing envelope that surrounds the central object(s

Coarse Grained Liouville Dynamics of piecewise linear discontinuous maps

We compute the spectrum of the classical and quantum mechanical coarse-grained propagators for a piecewise linear discontinuous map. We analyze the quantum - classical correspondence and the evolution of the spectrum with increasing resolution. Our results are compared to the ones obtained for a mixed system.Comment: 11 pages, 8 figure

Quantum Process Tomography of the Quantum Fourier Transform

The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently-developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive - although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors during the quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cummulative effect of small errors in the single qubit gates.Comment: 26 pages, 17 figures, four tables; in press, Journal of Chemical Physic