Symmetry and nonexistence of positive solutions for fractional systems

This paper is devoted to study the nonexistence results of positive solutions for the following fractional H$\acute{e}$non system \begin{eqnarray*}\left\{ \begin{array}{lll} &(-\triangle)^{\alpha/2}u=|x|^av^p,~~~&x\in R^n, &(-\triangle)^{\alpha/2}v=|x|^bu^q,~~~ &x\in R^n, &u\geq0, v\geq 0, \end{array} \right. \end{eqnarray*} where $0<\alpha<2$, $0<p,q<\infty$, $a$, $b$ $\geq0$, $n\geq2$. Using a direct method of moving planes, we prove non-existence of positive solution in the subcritical case

Nonadiabatic geometric rotation of electron spin in a quantum dot by 2Pi hyperbolic secant pulses

In this paper, the geometric and dynamic phase components of overall phase induced by 2{\pi} hyperbolic secant pulses in a quantum dot is analyzed. The dependence of two phase components on the ratio of the Rabi frequency to the detuning is investigated. Numerical results indicate that only for one resonant pulse the induced overall phase is purely the geometric phase. With other values of the ratio the overall phase consists of a nonzero dynamic part. The effect of spin precession to decrease the dynamic phase is characterized and discussed by analytical and numerical techniques. Utilizing the symmetry relations of the phases, a scheme to eliminate the dynamic phase by multipulse control is proposed. By choosing the proper parameter for each pulse, the dynamic phases induced by different pulses cancel out. The total pure geometric phase varies from -{\pi} to {\pi}, which realizes the arbitrary geometric rotation of spin. Average fidelity is calculated and the effects of magnetic field and decay of the trion state are compared and discussed. The results show the crucial role of weak magnetic field for high fidelity (above 99.3%).Comment: 7 pages, 8 figures, 1 tabl

Towards practical high-speed high dimensional quantum key distribution using partial mutual unbiased basis of photon's orbital angular momentum

Quantum Key Distribution (QKD) guarantees the security of communication with quantum physics. Most of widely adopted QKD protocols currently encode the key information with binary signal format---qubit, such as the polarization states. Therefore the transmitted information efficiency of the quantum key is intrinsically upper bounded by 1 bit per photon. High dimensional quantum system is a potential candidate for increasing the capacity of single photon. However, due to the difficulty in manipulating and measuring high dimensional quantum systems, the experimental high dimensional QKD is still at its infancy. Here we propose a sort of practical high-speed high dimensional QKD using partial mutual unbiased basis (PMUB) of photon's orbital angular momentum (OAM). Different from the previous OAM encoding, the high dimensional Hilbert space we used is expanded by the OAM states with same mode order, which can be extended to considerably high dimensions and implemented under current state of the art. Because all the OAM states are in the same mode order, the coherence will be well kept after long-distance propagation, and the detection can be achieved by using passive linear optical elements with very high speed. We show that our protocol has high key generation rate and analyze the anti-noise ability under atmospheric turbulence. Furthermore, the security of our protocol based on PMUB is rigorously proved. Our protocol paves a brand new way for the application of photon's OAM in high dimensional QKD field, which can be a breakthrough for high efficiency quantum communications.Comment: Comments are welcom

Shot cutoff timescales in different spectral states of Cygnus X-1

We investigate the shot cutoff timescale evolutions during different spectral states in the black hole binary Cygnus X-1 with the recently proposed w spectral analysis technique. For low energy shots, their cutoff timescale decreases from the low state to intermediate state, and to high state monotonically. However in the high energy range, where shots are believed to be reprocessed in the hot corona, timescales are almost the same for different spectral states. A linear correlation is found between the energy spectrum photon index and the shot cutoff timescale at low energies. Both narrow and broad iron Kalpha lines are distinguished from timing analysis, providing dynamical evidence that broad and narrow iron lines originate respectively at small and large radii of the accretion disk. Possible mechanisms for state transitions and accretion flow geometry in accreting stellar mass black holes are discussed.Comment: accepted for publication in ApJ

Model-independent determination of curvature parameter by using H(z)H(z) and DA(z)D_A(z) data pair from BAO measurement

We present a model-independent determination of the curvature parameter $\Omega_k$ by using the Hubble parameter $H(z)$ and angular diameter distance $D_A(z)$ from the recent baryon acoustic oscillation (BAO) measurements. Each $H(z)$ and $D_A(z)$ pair from a BAO measurement can constrain a curvature parameter. The accuracy of the curvature measurement improves with increased redshift of $H(z)$ and $D_A(z)$ data. By using the $H(z)$ and $D_A(z)$ pair derived from BAO Lyman $\alpha$ forest measurement at $z=2.36$, the $\Omega_k$ is confined to be -0.05$\pm$0.06, which is consistent with the curvature $-0.037^{+0.044}_{-0.042}$ constrained by the nine-year WMAP data only. Considering future BAO meausurements, at least one order of magnitude improvement of this curvature measurement could be expected.Comment: 5 pages, 3 figures. Accepted for publication in ApJ

Design and performance of an absolute gas refractometer based on quasi-synthetic wavelength method

We present a refractometer which is capable of measuring the refractive index of gas with an unambiguous range of 1.000395 and uncertainty of 3.1E-8 at 633 nm absolutely. The measurement range is extended by means of a group of vacuum tubes according to the principle of quasi-synthetic wavelength (QSW) method. The basic principle of the QSW method and the design of the gas refractometer are presented in detail. The performance of the refractometer has been verified by the measurement of dry air, nitrogen gas and ambient air under different environmental situations. The gas-filling or pumping process is not needed during the measurement, so that we can complete a measurement within 70 seconds. Comparing with previous ones, the refractometer reported here has integrated virtues of large unambiguous range, fast speed, high accuracy, and a simple instrumentation design.Comment: 12 pages,7 figure

Control excitation and coherent transfer in a dimer

In this article, the processes of energy absorption and coherent transfer in a dimer is studied. The dimer includes two two-level pigments --- donor and acceptor, where donor is assumed being excited by a control pulse in the time domain. We investigate the dynamics of probability that the acceptor is in the excited state and the total efficiency of energy absorption and transfer under different temporal shape of control pulse. Quantum concurrence of the dimer is also discussed

Super sub-wavelength patterns in photon coincidence detection

High-precision measurements implemented by means of light is desired in all fields of science. However, light is a wave and Rayleigh criterion gives us a diffraction limitation in classical optics which restricts to get arbitrary high resolution. Sub-wavelength interference has a potential application in lithography to beat the classical Rayleigh limit of resolution. We carefully study the second-order correlation theory to get the physics behind sub-wavelength interference in photon coincidence detection. A Young's double-slit experiment with pseudo-thermal light is carried out to test the second-order correlation pattern. The result shows that when different scanning ways of two point detectors are chosen, one can get super sub-wavelength interference patterns. We then give a theoretical explanation to this surprising result, and find this explanation is also suitable for the result by using entangled light. Furthermore, we discuss the limitation of this kind of super sub-wavelength interference patterns in quantum lithography.Comment: 5 pages, 5 figures, comments are welcom

Far-Infrared Spectroscopy of Cationic Polycyclic Aromatic Hydrocarbons: Zero Kinetic Energy Photoelectron Spectroscopy of Pentacene Vaporized from Laser Desorption

The distinctive set of infrared (IR) emission bands at 3.3, 6.2, 7.7, 8.6, and 11.3{\mu}m are ubiquitously seen in a wide variety of astrophysical environments. They are generally attributed to polycyclic aromatic hydrocarbon (PAH) molecules. However, not a single PAH species has yet been identified in space, as the mid-IR vibrational bands are mostly representative of functional groups and thus do not allow one to fingerprint individual PAH molecules. In contrast, the far-IR (FIR) bands are sensitive to the skeletal characteristics of a molecule, hence they are important for chemical identification of unknown species. With an aim to offer laboratory astrophysical data for the Herschel Space Observatory, Stratospheric Observatory for Infrared Astronomy, and similar future space missions, in this work we report neutral and cation FIR spectroscopy of pentacene (C_22H_14), a five-ring PAH molecule. We report three IR active modes of cationic pentacene at 53.3, 84.8, and 266{\mu}m that may be detectable by space missions such as the SAFARI instrument on board SPICA. In the experiment, pentacene is vaporized from a laser desorption source and cooled by a supersonic argon beam. We have obtained results from two-color resonantly enhanced multiphoton ionization and two-color zero kinetic energy photoelectron (ZEKE) spectroscopy. Several skeletal vibrational modes of the first electronically excited state of the neutral species and those of the cation are assigned, with the aid of ab initio and density functional calculations.Comment: 27 pages, 5 figures, 4 tables; published in Ap

Eclipse: Practicability Beyond kNN and Skyline

The $k$ nearest neighbor ($k$NN) query is a fundamental problem in databases. Given a set of multidimensional data points and a query point, $k$NN returns the $k$ nearest neighbors based on a scoring function such as weighted sum given an attribute weight vector. However, the attribute weight vector can be difficult to specify in practice. Skyline returns the points including all possible nearest neighbors without requiring the exact attribute weight vector or a scoring function but the number of returned points can be prohibitively large for practical use. In this paper, we propose a novel \emph{eclipse} definition which provides a more flexible and customizable definition than the classic $1$NN and skyline. In eclipse, users can specify a range of attribute weights and control the number of returned points. We show that both $1$NN and skyline are instantiations of eclipse. To compute eclipse points, we propose a baseline algorithm with time complexity of $O(n^22^{d-1})$, and an improved $O(n\log ^{d-1}n)$ time transformation-based algorithm by transforming the eclipse problem to the skyline problem, where $n$ is the number of points and $d$ is the number of dimensions. Furthermore, we propose a novel index-based algorithm utilizing duality transform with much better efficiency. The experimental results on the real NBA dataset and the synthetic datasets demonstrate the effectiveness and efficiency of our eclipse algorithms