Continuous-variable phase-estimation with unitary and random linear disturbance

We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level, by means of Gaussian probe states. In particular we discuss both unitary and random disturbance, by considering the parameter which characterizes the unwanted linear term present in the Hamiltonian as fixed (unitary disturbance) or random with a given probability distribution (random disturbance). We derive the optimal input Gaussian states at fixed energy, maximizing the quantum Fisher information over the squeezing angle and the squeezing energy fraction, and we discuss the scaling of the quantum Fisher information in terms of the output number of photons $n_{out}$. We observe that in the case of unitary disturbance the optimal state is a squeezed vacuum state and the quadratic scaling is conserved. As regards the random disturbance, we observe that the optimal squeezing fraction may not be equal to one, and, for any non-zero value of the noise parameter, the quantum Fisher information scales linearly with the average number of photons. We finally discuss the performance of homodyne measurement, comparing the achievable precision with the ultimate limit posed by the quantum Cram\'er-Rao bound.Comment: 7 pages, 6 figure

Probing variability patterns of the Fe K line complex in bright nearby AGNs

The unprecedented sensitivity of current X-ray telescopes allows for the first time to address the issue of the Fe K line complex variability patterns in bright, nearby AGNs. We examine XMM-Newton observations of the brightest sources of the FERO sample of radio-quiet type 1 AGNs with the aim of characterizing the temporal behaviour of Fe K complex features. A systematic mapping of residual flux above and below the continuum in the 4-9 keV range is performed in the time vs energy domain, with the purpose of identifying interesting spectral features in the three energy bands: 5.4-6.1 keV, 6.1-6.8 keV and 6.8-7.2 keV, corresponding respectively to the redshifted, rest frame and blueshifted or highly ionized Fe Kalpha line bands. The variability significance is assessed by extracting light curves and comparing them with MonteCarlo simulations. The time-averaged profile of the Fe K complex revealed spectral complexity in several observations. Red- and blue-shifted components (either in emission or absorption) were observed in 30 out of 72 observations, with an average ~90 eV for emission and ~ -30 eV for absorption features. We detected significant line variability (with confidence levels ranging between 90% and 99.7%) within at least one of the above energy bands in 26 out of 72 observations on time scales of ~6-30 ks. Reliability of these features has been carefully calculated using this sample and has been assessed at ~3sigma confidence level. This work increases the currently scanty number of detections of variable, energy shifted, Fe lines and confirms the reliability of the claimed detections. We found that the distribution of detected features is peaked at high variability significances in the red- and blue-shifted energy bands, suggesting an origin in a relativistically modified accretion flow.Comment: Accepted for publication in Astronomy & Astrophysic

The effect of a nucleating agent on lamellar growth in melt-crystallizing polyethylene oxide

The effects of a (non co-crystallizing) nucleating agent on secondary nucleation rate and final lamellar thickness in isothermally melt-crystallizing polyethylene oxide are considered. SAXS reveals that lamellae formed in nucleated samples are thinner than in the pure samples crystallized at the same undercoolings. These results are in quantitative agreement with growth rate data obtained by calorimetry, and are interpreted as the effect of a local decrease of the basal surface tension, determined mainly by the nucleant molecules diffused out of the regions being about to crystallize. Quantitative agreement with a simple lattice model allows for some interpretation of the mechanism.Comment: submitted to Journal of Applied Physics (first version on 22 Apr 2002

Completeness on the worm domain and the M\"untz-Sz\'asz problem for the Bergman space

In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain $\mathcal{W}_\mu$ and its truncated version $\mathcal{W}'_\mu$. We determine some orthogonal systems and show that they are not complete, while showing that the union of two particular of such systems is complete. In order to prove our completeness result we introduce the Muentz-Szasz problem for the 1-dimensional Bergman space of the disk $\{\zeta : |\zeta-1|<1\}$ and find a sufficient condition for its solution.Comment: 14 pages, Author Accepted Manuscrip

Swimmers in thin films: from swarming to hydrodynamic instabilities

We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses (force dipoles or quadrupoles) on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to the collective behaviour. In contrast, for quadrupolar swimmers, our analysis shows that detailed features of the internal dynamics play an important role in determining the bulk behaviour. In the broken symmetry phases, we investigate fluctuations of hydrodynamic variables of the system and find that these destabilize order. Interestingly, this instability is not generic and depends on length-scale.Comment: 4 pages, 2 figures, references added, typos corrected, new introductio

The very faint hard state of the persistent neutron star X-ray binary SLX 1737-282 near the Galactic centre

We report on a detailed study of the spectral and temporal properties of the neutron star low mass X-ray binary SLX 1737-282, which is located only ~1degr away from Sgr A. The system is expected to have a short orbital period, even within the ultra-compact regime, given its persistent nature at low X-ray luminosities and the long duration thermonuclear burst that it has displayed. We have analysed a Suzaku (18 ks) observation and an XMM-Newton (39 ks) observation taken 7 years apart. We infer (0.5-10 keV) X-ray luminosities in the range 3-6 x10^35erg s-1, in agreement with previous findings. The spectra are well described by a relatively cool (kTbb = 0.5 keV) black body component plus a Comptonized emission component with {\Gamma} ~1.5-1.7. These values are consistent with the source being in a faint hard state, as confirmed by the ~ 20 per cent fractional root mean square amplitude of the fast variability (0.1 - 7 Hz) inferred from the XMM-Newton data. The electron temperature of the corona is >7 keV for the Suzaku observation, but it is measured to be as low as ~2 keV in the XMM-Newton data at higher flux. The latter is significantly lower than expected for systems in the hard state. We searched for X-ray pulsations and imposed an upper limit to their semi-amplitude of 2 per cent (0.001 - 7 Hz). Finally, we investigated the origin of the low frequency variability emission present in the XMM-Newton data and ruled out an absorption dip origin. This constraint the orbital inclination of the system to 65 degr unless the orbital period is longer than 11 hr (i.e. the length of the XMM-Newton observation).Comment: 7 pages, 4 figures, 1 table. Accepted for publication in MNRA