The role of the diffusive protons in the gamma-ray emission of supernova remnant RX J1713.7−-3946 --- a two-zone model

RX~J1713.7$-$3946 is a prototype in the $\gamma$-ray-bright supernova remnants (SNRs) and is in continuing debates on its hadronic versus leptonic origin of the $\gamma$-ray emission. We explore the role played by the diffusive relativistic protons that escape from the SNR shock wave in the $\gamma$-ray emission, apart from the high-energy particles' emission from the inside of the SNR. In the scenario that the SNR shock propagates in a clumpy molecular cavity, we consider that the$\gamma$-ray emission from the inside of the SNR may arise either from the inverse Compton scattering or from the interaction between the trapped energetic protons and the shocked clumps. The dominant origin between them depends on the electron-to-proton number ratio. The diffusive protons that escaped from the shock wave during the expansion history can provide an outer hadronic $\gamma$-ray component by bombarding the surrounding dense matter. The broadband spectrum can be well explained by this two-zone model, in which the $\gamma$-ray emission from the inside governs the TeV band, while the outer emission component substantially contributes to the GeV $\gamma$-rays. The two-zone model can also explain the TeV $\gamma$-ray radial brightness profile that significantly stretches beyond the nonthermal X-ray-emitting region. In the calculation, we present a simplified algorithm for Li & Chen's (2010) "accumulative diffusion" model for escaping protons and apply the Markov Chain Monte Carlo method to constrain the physical parameters.Comment: 18 pages (including 3 figures and 2 tables), accepted for publication in Ap

m-Order Time Optimal Control Synthesis Function of Discrete System

In this paper, first of all, we introduce the basic concepts of generating function in combinatorics and some combinatorial identities. In order to facilitate the understanding of m-order time optimal control synthesis function of discrete system (referred as m-order synthesis function), secondly, we introduce the derivation process and control ideas of 2nd-order synthesis function, and then deduce in detail the m-order synthesis function by means of generating function. By use of the m-order tracking-form synthesis function with filter factor, the methods of signal extraction and its predictive compensation are presented in this paper, and their immunity and effectiveness are verified by numerical simulation.Comment: 22 pages,13 figures. arXiv admin note: substantial text overlap with arXiv:1806.0310

A Tensor Completion Approach for Efficient and Robust Fingerprint-based Indoor Localization

The localization technology is important for the development of indoor location-based services (LBS). The radio frequency (RF) fingerprint-based localization is one of the most promising approaches. However, it is challenging to apply this localization to real-world environments since it is time-consuming and labor-intensive to construct a fingerprint database as a prior for localization. Another challenge is that the presence of anomaly readings in the fingerprints reduces the localization accuracy. To address these two challenges, we propose an efficient and robust indoor localization approach. First, we model the fingerprint database as a 3-D tensor, which represents the relationships between fingerprints, locations and indices of access points. Second, we introduce a tensor decomposition model for robust fingerprint data recovery, which decomposes a partial observation tensor as the superposition of a low-rank tensor and a spare anomaly tensor. Third, we exploit the alternating direction method of multipliers (ADMM) to solve the convex optimization problem of tensor-nuclear-norm completion for the anomaly case. Finally, we verify the proposed approach on a ground truth data set collected in an office building with size 80m times 20m. Experiment results show that to achieve a same error rate 4%, the sampling rate of our approach is only 10%, while it is 60% for the state-of-the-art approach. Moreover, the proposed approach leads to a more accurate localization (nearly 20%, 0.6m improvement) over the compared approach.Comment: 6 pages, 5 figure

Observational Constraints on Two-field Warm Inflation

We study the two-field warm inflation models with a double quadratic potential and a linear temperature dependent dissipative coefficient. We derived the evolution equation of all kinds of perturbations without assuming slow-roll approximation, and obtained the curvature power spectrum at the end of inflation with a fully numerical method. Then we compute the scalar spectral index $n_s$, tensor-to-scalar ratio $r$ for several representative potentials, and compare our results with observational data. At last, we use Planck data to constrain the parameters in our models. This work is a natural extension of single-field warm inflation, and the aim of this work is to present some features of multi-field warm inflation using a simple two-field model.Comment: 13 pages, 6 figures. Accepted for publication in Physical Review

Two-field Warm Inflation and Its Scalar Perturbations on Large Scales

We explore the homogeneous background dynamics and the evolution of generated perturbations of cosmological inflation that is driven by multiple scalar fields interacting with a perfect fluid.Then we apply the method to warm inflation driven by two scalar fields and a radiation fluid, and present general results about the evolution of the inflaton and radiation. After decomposing the perturbations into adiabatic and entropy modes, we give the equation of motion of adiabatic and entropy perturbations on large scales. Then, we give numerical results of background and perturbation equations in a concrete model (the dissipative coefficient $\Gamma \propto H$). At last, we use the most recent observational data to constrain our models and give the observationally allowed regions of parameters. This work is a natural extension of warm inflation to multi-field cases.Comment: 10 pages, 4 figure

Lossy Quantum Optical Metrology with Squeezed States

We study the precise phase estimation using squeezed states with photon losses present. Our exact quantum Fisher information calculation shows significant quantum enhancement and thus reveals the benchmark for practical quantum metrology in this noisy scenario. However, we find that the existing parity measurement scheme [P.M. Anisimov et al, Phys. Rev. Lett. 104, 103602 (2010)] behaves worse than even classical cases given very small losses, unless we take an appropriate loss dependent phase shift. Using our formulae, the two optimized aspects including the pre-detection phase shift and the consequent light intensity of a tradeoff strategy for photon resource arrangement can be both calculated. Therefore our result makes it possible to experimentally realize quantum metrology of phase estimation with squeezed states.Comment: Published versio

Primordial non-Gaussianity in noncanonical warm inflation

We study the bispectrum of the primordial curvature perturbation on uniform-density hypersurfaces generated by a kind of the noncanonical warm inflation, wherein the inflation is provided by a noncanonical scalar inflaton field that is coupled to radiation through a thermal dissipation effect. We obtain an analytic form for the nonlinear parameter $f_{NL}$ that describes the non-Gaussianity in first-order cosmological perturbation theory and analyse the magnitude of this nonlinear parameter. We make a comparison between our result and those of the standard inflation and the canonical warm inflation. We also discuss when the contribution to the non-Gaussianity due to the second-order perturbation theory becomes more important and what effect can be observed. We take the Dirac-Born-Infeld (DBI) inflation as a concrete example to find how the sound speed and the thermal dissipation strength to decide the non-Gaussianity and to get a lower bound of the sound speed constrained by PLANCK.Comment: 7 pages, 2 figure

Warm inflation in loop quantum cosmology: a model with a general dissipative coefficient

A general form of warm inflation with the dissipative coefficient $\Gamma=\Gamma_0(\phi /\phi_0) ^n(T/\tau_0) ^m$ in loop quantum cosmology is studied. In this case, we obtain conditions for the existence of a warm inflationary attractor in the context of loop quantum cosmology by using the method of stability analysis. The two cases when the dissipative coefficient is independent $(m=0)$ and dependent $(m\neq0)$ on temperature are analyzed specifically. In the latter case, we use the new power spectrum which should be used when considering temperature dependence in the dissipative coefficient. We find that the thermal effect is enhanced in the case $m>0$. As in the standard inflation in loop quantum cosmology, we also reach the conclusion that quantum effect leaves a tiny imprint on the cosmic microwave background (CMB) sky.Comment: 12 pages, accepted for publication in Rhys. Rev.

The diagram category of framed tangles and invariants of quantized symplectic group

In this paper we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups. Our methods depend on the theory of braided strict monoidal categories which are pivotal, more explicitly the diagram category of framed tangles.Comment: to appear in Sci. China Mat

Consistency of the tachyon warm inflationary universe models

This study concerns the consistency of the tachyon warm inflationary models. A linear stability analysis is performed to find the slow-roll conditions, characterized by the potential slow-roll (PSR) parameters, for the existence of a tachyon warm inflationary attractor in the system. The PSR parameters in the tachyon warm inflationary models are redefined. Two cases, an exponential potential and an inverse power-law potential, are studied, when the dissipative coefficient $\Gamma=\Gamma_0$ and $\Gamma=\Gamma(\phi)$, respectively. A crucial condition is obtained for a tachyon warm inflationary model characterized by the Hubble slow-roll (HSR) parameter $\epsilon_{_H}$, and the condition is extendable to some other inflationary models as well. A proper number of e-folds is obtained in both cases of the tachyon warm inflation, in contrast to existing works. It is also found that a constant dissipative coefficient $(\Gamma=\Gamma_0)$ is usually not a suitable assumption for a warm inflationary model.Comment: 10 pages, 0 figures, accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP