Direct Measurement of Kirkwood-Rihaczek distribution for spatial properties of coherent light beam

We present direct measurement of Kirkwood-Rihaczek (KR) distribution for spatial properties of coherent light beam in terms of position and momentum (angle) coordinates. We employ a two-local oscillator (LO) balanced heterodyne detection (BHD) to simultaneously extract distribution of transverse position and momentum of a light beam. The two-LO BHD could measure KR distribution for any complex wave field (including quantum mechanical wave function) without applying tomography methods (inverse Radon transformation). Transformation of KR distribution to Wigner, Glauber Sudarshan P- and Husimi or Q- distributions in spatial coordinates are illustrated through experimental data. The direct measurement of KR distribution could provide local information of wave field, which is suitable for studying particle properties of a quantum system. While Wigner function is suitable for studying wave properties such as interference, and hence provides nonlocal information of the wave field. The method developed here can be used for exploring spatial quantum state for quantum mapping and computing, optical phase space imaging for biomedical applications.Comment: 27 pages, 14 figure

Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C^n tensor C^n whose operator-Schmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number S for every S in {1,...,9}. This corollary was unexpected, since it contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003) 052301] based on intuition from a striking result in the two-qubit case. By the results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901 quant-ph/0112124], who also considered the two-qubit case, our result implies that there are nine equivalence classes of unitaries on C^3 tensor C^3 which are probabilistically interconvertible by (stochastic) local operations and classical communication. As another corollary, a prescription is produced for constructing maximally-entangled operators from biunimodular functions. Reversing tact, we state a generalized operator-Schmidt decomposition of the quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 --> C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by Nielsen's bound) that the communication cost of the QFT remains maximal when a net transfer of qudits is permitted. In an appendix, a canonical procedure is given for removing basis-dependence for results and proofs depending on the "magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and quant-ph/9709029)].Comment: More formal version of my talk at the Simons Conference on Quantum and Reversible Computation at Stony Brook May 31, 2003. The talk slides and audio are available at http://www.physics.sunysb.edu/itp/conf/simons-qcomputation.html. Fixed typos and minor cosmetic

A First Look at CQVID-19 Messages on WhatsApp in Pakistan

The worldwide spread of COVID-19 has prompted extensive online discussions, creating an `infodemic' on social media platforms such as WhatsApp and Twitter. However, the information shared on these platforms is prone to be unreliable and/or misleading. In this paper, we present the first analysis of COVID-19 discourse on public WhatsApp groups from Pakistan. Building on a large scale annotation of thousands of messages containing text and images, we identify the main categories of discussion. We focus on COVID-19 messages and understand the different types of images/text messages being propagated. By exploring user behavior related to COVID messages, we inspect how misinformation is spread. Finally, by quantifying the flow of information across WhatsApp and Twitter, we show how information spreads across platforms and how WhatsApp acts as a source for much of the information shared on Twitter

Behavioral implications of shortlisting procedures

We consider two-stage “shortlisting procedures” in which the menu of alternatives is first pruned by some process or criterion and then a binary relation is maximized. Given a particular first-stage process, our main result supplies a necessary and sufficient condition for choice data to be consistent with a procedure in the designated class. This result applies to any class of procedures with a certain lattice structure, including the cases of “consideration filters,” “satisficing with salience effects,” and “rational shortlist methods.” The theory avoids background assumptions made for mathematical convenience; in this and other respects following Richter’s classical analysis of preference-maximizing choice in the absence of shortlisting

Temporal variability and statistics of the Strehl ratio in adaptive-optics images

We have investigated the temporal variability and statistics of the "instantaneous" Strehl ratio. The observations were carried out with the 3.63-m AEOS telescope equipped with a high-order adaptive optics system. In this paper Strehl ratio is defined as the peak intensity of a single short exposure. We have also studied the behaviour of the phase variance computed on the reconstructed wavefronts. We tested the Marechal approximation and used it to explain the observed negative skewness of the Strehl ratio distribution. The estimate of the phase variance is shown to fit a three-parameter Gamma distribution model. We show that simple scaling of the reconstructed wavefronts has a large impact on the shape of the Strehl ratio distribution.Comment: submitted to PAS

Size-selective nanoparticle growth on few-layer graphene films

We observe that gold atoms deposited by physical vapor deposition onto few layer graphenes condense upon annealing to form nanoparticles with an average diameter that is determined by the graphene film thickness. The data are well described by a theoretical model in which the electrostatic interactions arising from charge transfer between the graphene and the gold particle limit the size of the growing nanoparticles. The model predicts a nanoparticle size distribution characterized by a mean diameter D that follows a scaling law D proportional to m^(1/3), where m is the number of carbon layers in the few layer graphene film.Comment: 15 pages, 4 figure

Notes on Conformal Invisibility Devices

As a consequence of the wave nature of light, invisibility devices based on isotropic media cannot be perfect. The principal distortions of invisibility are due to reflections and time delays. Reflections can be made exponentially small for devices that are large in comparison with the wavelength of light. Time delays are unavoidable and will result in wave-front dislocations. This paper considers invisibility devices based on optical conformal mapping. The paper shows that the time delays do not depend on the directions and impact parameters of incident light rays, although the refractive-index profile of any conformal invisibility device is necessarily asymmetric. The distortions of images are thus uniform, which reduces the risk of detection. The paper also shows how the ideas of invisibility devices are connected to the transmutation of force, the stereographic projection and Escheresque tilings of the plane

Theory of Spike Spiral Waves in a Reaction-Diffusion System

We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of these waves in Gray-Scott model. We derive the kinematic relations describing the shape of this spiral and find the dependence of its main parameters on the control parameters. The theory does not rely on the specific features of Gray-Scott model and thus is expected to be applicable to a broad range of reaction-diffusion systems.Comment: 4 pages (REVTeX), 2 figures (postscript), submitted to Phys. Rev. Let

Parametrization and Classification of 20 Billion LSST Objects: Lessons from SDSS

The Large Synoptic Survey Telescope (LSST) will be a large, wide-field ground-based system designed to obtain, starting in 2015, multiple images of the sky that is visible from Cerro Pachon in Northern Chile. About 90% of the observing time will be devoted to a deep-wide-fast survey mode which will observe a 20,000 deg$^2$ region about 1000 times during the anticipated 10 years of operations (distributed over six bands, $ugrizy$). Each 30-second long visit will deliver 5$\sigma$ depth for point sources of $r\sim24.5$ on average. The co-added map will be about 3 magnitudes deeper, and will include 10 billion galaxies and a similar number of stars. We discuss various measurements that will be automatically performed for these 20 billion sources, and how they can be used for classification and determination of source physical and other properties. We provide a few classification examples based on SDSS data, such as color classification of stars, color-spatial proximity search for wide-angle binary stars, orbital-color classification of asteroid families, and the recognition of main Galaxy components based on the distribution of stars in the position-metallicity-kinematics space. Guided by these examples, we anticipate that two grand classification challenges for LSST will be 1) rapid and robust classification of sources detected in difference images, and 2) {\it simultaneous} treatment of diverse astrometric and photometric time series measurements for an unprecedentedly large number of objects.Comment: Presented at the "Classification and Discovery in Large Astronomical Surveys" meeting, Ringberg Castle, 14-17 October, 200

Rough droplet model for spherical metal clusters

We study the thermally activated oscillations, or capillary waves, of a neutral metal cluster within the liquid drop model. These deformations correspond to a surface roughness which we characterize by a single parameter $\Delta$. We derive a simple analytic approximate expression determining $\Delta$ as a function of temperature and cluster size. We then estimate the induced effects on shell structure by means of a periodic orbit analysis and compare with recent data for shell energy of sodium clusters in the size range $50 < N < 250$. A small surface roughness $\Delta\simeq 0.6$ \AA~ is seen to give a reasonable account of the decrease of amplitude of the shell structure observed in experiment. Moreover -- contrary to usual Jahn-Teller type of deformations -- roughness correctly reproduces the shape of the shell energy in the domain of sizes considered in experiment.Comment: 20 pages, 4 figures, important modifications of the presentation, to appear in Phys. Rev.