A Unique Method to Determine SNe Initial Explosion Energy

There are several different methods to determine the individual supernovae (SNe) initial explosion energy, here we derive the average or typical explosion energy of shell-type supernova remnants (SNRs) in a particular way. By solving a group of equations pertaining to shell-type SNRs at the same stage we obtained some physical parameters, e.g. the distance ($d$), evolved age ($t$), etc.. Assuming series of different SN initial explosion energies ranging from $10^{48}$ ergs to $10^{53}$ ergs, we derived series of distance and age parameters with which compared already known ones. Thus the most likely value of the SNe initial explosion energy is obtained when the deviation is least, which equals to about $10^{51}$ ergs, in good agreement with the undertook value.Comment: 12 pages, 6 figure

Distances to Two Galactic Supernova Remnants: G32.8-0.1 and G346.6-0.2

There are either a near kinematic distance of 5.5 kpc or a far distance of 8.8 kpc for a Galactic supernova remnant (SNR) G32.8$-$0.1 derived by using the rotation curve of the Galaxy. Here we make sure that the remnant distance is the farther one 8.8 kpc through solving a group of equations for the shell-type remnants separately at the adiabatic-phase and the radiative-phase. For SNR G346.6$-$0.2 we determine its distance also the farther one 11 kpc rather than the nearer one 5.5 kpc.Comment: 5 pages, 3 figure

The effect of in-plane magnetic field and applied strain in quantum spin Hall systems: application to InAs/GaSb quantum wells

Motivated by the recent discovery of quantized spin Hall effect in InAs/GaSb quantum wells\cite{du2013}$^,$\cite{xu2014}, we theoretically study the effects of in-plane magnetic field and strain effect to the quantization of charge conductance by using Landauer-Butikker formalism. Our theory predicts a robustness of the conductance quantization against the magnetic field up to a very high field of 20 tesla. We use a disordered hopping term to model the strain and show that the strain may help the quantization of the conductance. Relevance to the experiments will be discussed.Comment: 8 pages, 10 figures. Comments are welcome

Real-world Noisy Image Denoising: A New Benchmark

Most of previous image denoising methods focus on additive white Gaussian noise (AWGN). However,the real-world noisy image denoising problem with the advancing of the computer vision techiniques. In order to promote the study on this problem while implementing the concurrent real-world image denoising datasets, we construct a new benchmark dataset which contains comprehensive real-world noisy images of different natural scenes. These images are captured by different cameras under different camera settings. We evaluate the different denoising methods on our new dataset as well as previous datasets. Extensive experimental results demonstrate that the recently proposed methods designed specifically for realistic noise removal based on sparse or low rank theories achieve better denoising performance and are more robust than other competing methods, and the newly proposed dataset is more challenging. The constructed dataset of real photographs is publicly available at \url{https://github.com/csjunxu/PolyUDataset} for researchers to investigate new real-world image denoising methods. We will add more analysis on the noise statistics in the real photographs of our new dataset in the next version of this article.Comment: 13 pages, 8 figures, 8 tables. arXiv admin note: text overlap with arXiv:1707.01313 by other author

Waiting times and stopping probabilities for patterns in Markov chains

Suppose that $\mathcal C$ is a finite collection of patterns. Observe a Markov chain until one of the patterns in $\mathcal C$ occurs as a run. This time is denoted by $\tau$. In this paper, we aim to give an easy way to calculate the mean waiting time $E(\tau)$ and the stopping probabilities $P(\tau=\tau_A)$ with $A\in\mathcal C$, where $\tau_A$ is the waiting time until the pattern $A$ appears as a run.Comment: 13 page

Exact Solution to Haldane-BCS-Hubbard Model Along the Symmetric Lines: Interaction Induced Topological Phase Transition

We propose a Haldane-BCS-Hubbard model on a honeycomb lattice, which is composed of two copies of the Haldane model of the quantum anomalous Hall effect, an equal-spin pairing term and an onsite Hubbard interaction term. For any interaction strength, this model is exactly solvable along the symmetric line where the hopping and pairing amplitudes are equal to each other. The ground state of the Haldane-BCS-Hubbard model is a topological superconducting state at weak interaction with two chiral Majorana edge states. A strong interaction drives the system across a topological quantum phase transition to a topologically trivial superconductor. A $\mathbb{Z}_{2}$ symmetry of the Hamiltonian, which is a composition of the bond-centered inversion and a gauge transformation, is spontaneously broken by the interaction, resulting a finite antiferromagnetic order in the $y$-direction.Comment: 9 pages, 7 figure

Theory for Spin Selective Andreev Reflection in Vortex Core of Topological Superconductor: Majorana Zero Modes on Spherical Surface and Application to Spin Polarized Scanning Tunneling Microscope Probe

Majorana zero modes (MZMs) have been predicted to exist in the topological insulator (TI)/superconductor (SC) heterostructure. Recent spin polarized scanning tunneling microscope (STM) experiment$^{1}$ has observed spin-polarization dependence of the zero bias differential tunneling conductance at the center of vortex core, which may be attributed to the spin selective Andreev reflection, a novel property of the MZMs theoretically predicted in 1-dimensional nanowire$^{2}$. Here we consider a helical electron system described by a Rashba spin orbit coupling Hamiltonian on a spherical surface with a s-wave superconducting pairing due to proximity effect. We examine in-gap excitations of a pair of vortices with one at the north pole and the other at the south pole. While the MZM is not a spin eigenstate, the spin wavefunction of the MZM at the center of the vortex core, r = 0, is parallel to the magnetic field, and the local Andreev reflection of the MZM is spin selective, namely occurs only when the STM tip has the spin polarization parallel to the magnetic field, similar to the case in 1-dimensional nanowire2. The total local differential tunneling conductance consists of the normal term proportional to the local density of states and an additional term arising from the Andreev reflection. We also discuss the finite size effect, for which the MZM at the north pole is hybridized with the MZM at the south pole. We apply our theory to examine the recently reported spin-polarized STM experiments and show good agreement with the experiments.Comment: 14 pages, 14 figures, 1 table. Comments are welcome

Orbital Feshbach Resonance: A "Wide" Narrow Resonance for Higher Transition Temperature Fermi Superfluid

In this letter we show that the recently theoretically predicted and experimentally observed "orbital Feshbach resonance" in alkali-earth-like Yb-173 atom is a narrow resonance in energy, while it is hundreds Gauss wide in term of magnetic field strength, taking the advantage that the magnetic moment difference between the open and closed channels is quite small. Therefore this is an ideal platform for the experimental realization of a strongly interacting Fermi superfluid with narrow resonance. We show that the transition temperature for the Fermi superfluid in this system, especially at the BCS side of the resonance, is even higher than that in a wide resonance, which is also due to the narrow character of this resonance. Our results will encourage experimental efforts to realize Fermi superfluid in the alkali-earth-like Yb-173 system, the properties of which will be complementary to extensively studied Fermi superfluids nearby a wide resonance in alkali K-40 and Li-6 systems.Comment: 10 pages, 5 figure

Codebook-Based Beam Tracking for Conformal ArrayEnabled UAV MmWave Networks

Millimeter wave (mmWave) communications can potentially meet the high data-rate requirements of unmanned aerial vehicle (UAV) networks. However, as the prerequisite of mmWave communications, the narrow directional beam tracking is very challenging because of the three-dimensional (3D) mobility and attitude variation of UAVs. Aiming to address the beam tracking difficulties, we propose to integrate the conformal array (CA) with the surface of each UAV, which enables the full spatial coverage and the agile beam tracking in highly dynamic UAV mmWave networks. More specifically, the key contributions of our work are three-fold. 1) A new mmWave beam tracking framework is established for the CA-enabled UAV mmWave network. 2) A specialized hierarchical codebook is constructed to drive the directional radiating element (DRE)-covered cylindrical conformal array (CCA), which contains both the angular beam pattern and the subarray pattern to fully utilize the potential of the CA. 3) A codebook-based multiuser beam tracking scheme is proposed, where the Gaussian process machine learning enabled UAV position/attitude predication is developed to improve the beam tracking efficiency in conjunction with the tracking-error aware adaptive beamwidth control. Simulation results validate the effectiveness of the proposed codebook-based beam tracking scheme in the CA-enabled UAV mmWave network, and demonstrate the advantages of CA over the conventional planner array in terms of spectrum efficiency and outage probability in the highly dynamic scenarios

Engineering of nonclassical motional states in optomechanical systems

We propose to synthesize arbitrary nonclassical motional states in optomechanical systems by using sideband excitations and photon blockade. We first demonstrate that the Hamiltonian of the optomechanical systems can be reduced, in the strong single-photon optomechanical coupling regime when the photon blockade occurs, to one describing the interaction between a driven two-level trapped ion and the vibrating modes, and then show a method to generate target states by using a series of classical pulses with desired frequencies, phases, and durations. We further analyze the effect of the photon leakage, due to small anharmonicity, on the fidelity of the expected motional state, and study environment induced decoherence. Moreover, we also discuss the experimental feasibility and provide operational parameters using the possible experimental data.Comment: 11 pages, 4 figure