Quantum Cloning, Bell's Inequality and Teleportation

We analyze a possibility of using the two qubit output state from Buzek-Hillery quantum copying machine (not necessarily universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter $\xi$ for which the two qubit output state is entangled and violates Bell-CHSH inequality and for a different range it remains entangled but does not violate Bell-CHSH inequality. Further we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Buzek-Hillery cloning machine as a teleportation channel provides an additional appeal to the cloning machine and motivation of our present work.Comment: 7 pages and no figures, Accepted in Journal of Physics

Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials

We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions give rise to nontopological (pulse-like) single solitons, as well as to different types of topological (kink-like) single soliton solutions of the Associated Lam\'e equation. Following Manton, we also compute, as an illustration, the asymptotic interaction energy between these soliton solutions in one particular case. Finally, in specific limits, we deduce the soliton lattices, as well as the topological single soliton solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy

Emergence of a non-scaling degree distribution in bipartite networks: a numerical and analytical study

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We derive the exact analytical expression for the degree-distribution of all these different types of attachments while assuming that edges are incorporated sequentially, i.e., a single edge is added to the growing network in a time step. We also provide an approximate expression for the case when more than one edge are added in a time step. We show that depending on the relative weight between random and preferential attachment, the degree-distribution of this type of network falls into one of four possible regimes which range from a binomial distribution for pure random attachment to an u-shaped distribution for dominant preferential attachment

On Deterministic Sketching and Streaming for Sparse Recovery and Norm Estimation

We study classic streaming and sparse recovery problems using deterministic linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the latter also being known as l1-heavy hitters), norm estimation, and approximate inner product. We focus on devising a fixed matrix A in R^{m x n} and a deterministic recovery/estimation procedure which work for all possible input vectors simultaneously. Our results improve upon existing work, the following being our main contributions: * A proof that linf/l1 sparse recovery and inner product estimation are equivalent, and that incoherent matrices can be used to solve both problems. Our upper bound for the number of measurements is m=O(eps^{-2}*min{log n, (log n / log(1/eps))^2}). We can also obtain fast sketching and recovery algorithms by making use of the Fast Johnson-Lindenstrauss transform. Both our running times and number of measurements improve upon previous work. We can also obtain better error guarantees than previous work in terms of a smaller tail of the input vector. * A new lower bound for the number of linear measurements required to solve l1/l1 sparse recovery. We show Omega(k/eps^2 + klog(n/k)/eps) measurements are required to recover an x' with |x - x'|_1 <= (1+eps)|x_{tail(k)}|_1, where x_{tail(k)} is x projected onto all but its largest k coordinates in magnitude. * A tight bound of m = Theta(eps^{-2}log(eps^2 n)) on the number of measurements required to solve deterministic norm estimation, i.e., to recover |x|_2 +/- eps|x|_1. For all the problems we study, tight bounds are already known for the randomized complexity from previous work, except in the case of l1/l1 sparse recovery, where a nearly tight bound is known. Our work thus aims to study the deterministic complexities of these problems

An HST/COS legacy survey of high-velocity ultraviolet absorption in the Milky Way's circumgalactic medium and the Local Group

To characterize the absorption properties of this circumgalactic medium (CGM) and its relation to the LG we present the so-far largest survey of metal absorption in Galactic high-velocity clouds (HVCs) using archival ultraviolet (UV) spectra of extragalactic background sources. The UV data are obtained with the Cosmic Origins Spectrograph (COS) onboard the Hubble Space Telescope (HST) and are supplemented by 21 cm radio observations of neutral hydrogen. Along 270 sightlines we measure metal absorption in the lines of SiII, SiIII, CII, and CIV and associated HI 21 cm emission in HVCs in the velocity range |v_LSR|=100-500 km s^-1. With this unprecedented large HVC sample we were able to improve the statistics on HVC covering fractions, ionization conditions, small-scale structure, CGM mass, and inflow rate. For the first time, we determine robustly the angular two point correlation function of the high-velocity absorbers, systematically analyze antipodal sightlines on the celestial sphere, and compare the absorption characteristics with that of Damped Lyman alpha absorbers (DLAs) and constrained cosmological simulations of the LG. Our study demonstrates that the Milky Way CGM contains sufficient gaseous material to maintain the Galactic star-formation rate at its current level. We show that the CGM is composed of discrete gaseous structures that exhibit a large-scale kinematics together with small-scale variations in physical conditions. The Magellanic Stream clearly dominates both the cross section and mass flow of high-velocity gas in the Milky Way's CGM. The possible presence of high-velocity LG gas underlines the important role of the local cosmological environment in the large-scale gas-circulation processes in and around the Milky Way (abridged).Comment: 37 pages, 25 figures, 8 tables, accepted for publication in A&

Impacts of the 20th January 2005 solar proton event on the ozone concentration of Indian cities

The ozone data obtained from Nimbus-7 and Earth probe Total Ozone Mapping Spectrometer (TOMS) has been used to study the impact of coronal mass ejection (CME) on the columnar ozone concentration in India. A comparison of columnar ozone values for different solar proton events (SPE) observed at Srinagar indicates that although the 20th Jan., 2005 SPE was the most intense in the last 15 years, the ozone depletion was found to be maximum in the 23rd March, 1991 event followed by 20th Jan., 2005, 4th Nov., 2001, 19th Oct., 1989 and 28th Oct., 2003 events. A comparison between the ozone levels observed in different Indian cities for a few days after the 20th Jan., 2005 SPE indicates that the ozone values were found to decrease sharply at higher latitudes compared to places located in the tropics .The ozone values measured by TOMS, Dobson Spectrometer and AURA Ozone Monitoring Instrument (OMI) were found to decrease for a short period from 20th January to 25th January after which the ozone levels started recovering to normal values. The vertical ozone profiles obtained from Microwave Limb Sounder for New Delhi, indicate that the ozonemixing ratio in the 3.0 to 10.0 hPa pressure range decreased consistently from 21st Jan., 2005 to 25th Jan., 2005 and thereafter, recovered by the 31st January, 2005.Impacts of the 20th January 2005 solar proton event on the ozone concentration of Indian cities Nandita D Ganguly 1* and K N Iyer 2 1 Department of Physics, St.Xavier’s College, Ahmedabad-380 009, Gujarat, India 2 Department of Physics, Saurashtra University, Rajkot-360 005, Gujarat, India E–mail: [email protected] Received 1 December 2005, accepted 27 February 20061 Department of Physics, St.Xavier’s College, Ahmedabad-380 009, Gujarat, India 2 Department of Physics, Saurashtra University, Rajkot-360 005, Gujarat, Indi