Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics

Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic schemes to relativistic charged particle dynamics result in implicit and electromagnetic gauge-dependent algorithms. In the present study, we develop explicit high-order gauge-independent noncanonical symplectic algorithms for relativistic charged particle dynamics using a Hamiltonian splitting method in the 8D phase space. It also shown that the developed algorithms can be derived as variational integrators by appropriately discretizing the action of the dynamics. Numerical examples are presented to verify the excellent long-term behavior of the algorithms.Comment: 8 figure

Structure-preserving geometric particle-in-cell algorithm suppresses finite-grid instability -- Comment on "Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm'' by Huang et al

A recent paper by Huang et al. [Computer Physics Communications 207, 123 (2016)] thoroughly analyzed the Finite Grid Instability(FGI) and spectral fidelity of standard Particle-In-Cell (PIC) methods. Numerical experiments were carried out to demonstrate the FGIs for two PIC methods, the energy-conserving algorithm and the momentum-conserving algorithm. The paper also suggested that similar numerical experiments should be performed to test the newly developed Structure-Preserving Geometric (SPG)-PIC algorithm. In this comment, we supply the results of the suggested numerical experiments, which show that the SPG-PIC algorithm is able to suppress the FGI

Signature of heavy sterile neutrinos at CEPC

We study the production of heavy sterile neutrino $N$, $e^+ e^- \to N \nu({\bar \nu})$, at the Circular Electron Positron Collider(CEPC) and its $ljj$ signal in its decay to three charged fermions. We study background events for this process which are mainly events coming from W pair production. We study the production of a single heavy sterile neutrino and the sensitivity of CEPC to the mixing of sterile neutrino with active neutrinos. We study the production of two degenerate heavy sterile neutrinos in a low energy see-saw model by taking into account the constraints on mixings of sterile neutrinos from the neutrino-less double $\beta$ decay experiment and the masses and mixings of active neutrinos. We show that CEPC under proposal has a good sensitivity to the mixing of sterile neutrinos with active neutrinos for a mass of sterile neutrino around 100 GeV.Comment: 24 pages, 11 figures, 1 table, published versio

Dynamical gap generation in 2D Dirac semimetal with deformed Dirac cone

According to the extensive theoretical and experimental investigations, it is widely accepted that the long-range Coulomb interaction is too weak to generate a dynamical excitonic gap in graphene with a perfect Dirac cone. We study the impact of the deformation of Dirac cone on dynamical gap generation. When a uniaxial strain is applied to graphene, the Dirac cone is made elliptical in the equal-energy plane and the fermion velocity becomes anisotropic. The applied uniaxial strain has two effects: it decreases the fermion velocity; it increases the velocity anisotropy. After solving the Dyson-Schwinger gap equation, we show that dynamical gap generation is promoted by the former effect, but is suppressed by the latter one. For suspended graphene, we find that the systems undergoes an excitonic insulating transition when the strain is roughly 7.34$\%$. We also solve the gap equation in case the Dirac cone is tiled, which might be realized in the organic material $\alpha$-(BEDT-TTF)$_{2}$I$_{3}$, and find that the tilt of Dirac cone can suppress dynamical gap generation. It turns out that the geometry of the Dirac cone plays an important role in the formation of excitonic pairing.Comment: 11 pages,11 figure

Charged lepton flavor violation on target at GeV scale

We study the lepton flavor violating process, $e+ T \to \tau +T'$, at a few GeV. This process can be studied by experiments directing GeV scale electron or positron beams on internal or fixed targets. We study the effects of some low energy lepton flavor violating interactions on this process. We study the sensitivities of this process on these low energy lepton flavor violating interactions and compare them to the sensitivities of lepton flavor violating $\tau$ decay processes. Comparing with $\tau$ decay processes, this process provides another way to study the lepton flavor violating effects with $e-\tau$ conversion and it can be searched for in facilities with GeV scale electron or positron beams which are available in a number of laboratories in the world.Comment: 22 pages, 4 figure

Mid-to-Far Infrared Spectral Energy Distribution of Galaxies in Spitzer First Look Survey Field

We made model fitting to the mid-to-far infrared spectral energy distributions (SEDs) for different categories of galaxies in the main extragalactic field of the {\it Spitzer} First Look Survey with the aid of spectroscopic information from the Sloan Digital Sky Survey. We find that the mid-to-far infrared SEDs of HII galaxies, mixture type galaxies and LINERs can be well fitted by the one-parameter ($\alpha$) dust model of Dale et al. plus the 13 Gyr dust-free elliptical galaxy model. The statistics of $\alpha$ values indicates that all these galaxies tend to be quiescent, although the HII galaxies are relatively more active than the LINERs. The mid-infrared SEDs of absorption galaxies are well fitted simply by the 13 Gyr dust-free elliptical galaxy template, and the near-to-mid infrared SEDs of QSOs can be represented by AGN NGC 5506.Comment: 12 pages with 8 figures, will be appeared in ChJAA, Vol.7 (2007), No.

Synchrotron spectrum of fast cooling electrons in GRBs

We discuss the synchrotron emission of fast cooling electrons in shocks. The fast cooling electrons behind the shocks can generate a position-dependent inhomogeneous electron distribution if they do not have enough time to mix homogeneously. This would lead to a very different synchrotron spectrum in low-frequency bands to that in the homogeneous case due to the synchrotron absorption. In this paper, we calculate the synchrotron spectrum in the inhomogeneous case in a gamma-ray burst (GRB). Both the forward shock and the reverse shock are considered. We find for the reverse shock dominated case, we would expect a "reverse shock bump" in the low-frequency spectrum. The spectral bump is due to the combination synchrotron absorption in both the forward and reverse shock regions. In the forward shock spectrum in the low frequencies has two unconventional segments with spectral slopes of $\lesssim1$ and $11/8$. The slope of $11/8$ has been found by some authors, while the slope of $\lesssim1$ is new, which is due to the approximately constant electron temperature in the optically thick region. In the future, simultaneous observations in multiple bands (especially in the low frequency bands) in the GRB early afterglow or prompt emission phases will possibly reveal these spectral characteristics and enable us to identify the reverse shock component and distinguish between the forward and reverse shock emissions. This also may be a method with which to diagnose the electron distribution status (homogeneous or inhomogeneous) after fast cooling in the relativistic shock region.Comment: Published in ApJ, 839, 74 (7pp), 2017, Apri

Canonical Form and Separability of PPT States on Multiple Quantum Spaces

By using the "subtracting projectors" method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in {\Cb}^{K_1} \otimes {\Cb}^{K_2} \otimes ... \otimes {\Cb}^{K_m} \otimes {\Cb}^N composite quantum systems with rank $N$, from which a sufficient separability condition for these states is presented.Comment: 5 page

PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability

We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regardless of whether it is diagonalizable or not. This result is different from Mostafazadeh's, which requires the Hamiltonian to be diagonalizable. PT-symmetry breaking often occurs at exceptional points where the Hamiltonian is not diagonalizable. Our result implies that PT-symmetry breaking is equivalent to the onset of instabilities of pseudo-Hermitian systems, which was systematically studied by Krein et al. in 1950s. In particular, we show that the mechanism of PT-symmetry breaking is the resonance between eigenmodes with different Krein signatures.Comment: 11pages, 1 figure. arXiv admin note: text overlap with arXiv:1801.0167

Double Electromagnetically Induced Transparency in a Tripod-type Atom System

The electromagnetically induced transparency (EIT) phenomenon in a four level atomic system with tripod configuration is studied. The results show that this configuration is equivalent to the combination of two single three-level $\Lambda$ configurations, which, under certain conditions, results in the so-called double-EIT (DEIT) phenomenon. The properties of the double transparency windows for DEIT are discussed in detail and the possible experimental scheme is proposed.Comment: 5 pages, and 8 figure