Duration distributions for different softness groups of gamma-ray bursts

Gamma-ray bursts(GRBs) are divided into two classes according to their durations.We investigate if the softness of bursts plays a role in the conventional classification of the objects.We employ the BATSE(Burst and Transient Source Experiment) catalog and analyze the duration distributions of different groups of GRBs associated with distinct softness.Our analysis reveals that the conventional classification of GRBs with the duration of bursts is influenced by the softness of the objects.There exists a bimodality in the duration distribution of GRBs for each group of bursts and the time position of the dip in the bimodality histogram shifts with the softness parameter.Our findings suggest that the conventional classification scheme should be modified by separating the two well-known populations in different softness groups,which would be more reasonable than doing so with a single sample.According to the relation between the dip position and the softness parameter,we get an empirical function that can roughly set apart the short-hard and long-soft bursts:SP =(0.100 ± 0.028) T-(0.85 0.18) 90,± where SP is the softness parameter adopted in this paper.     

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

We study the evolution properties of spin-boson systems by a systematic numerical iteration approach, which performs well in the whole coupling regime. This approach evaluates a set of coefficients in the formal expression of the time-dependent Schr?dinger equation by expanding the initial state in Fock space. This set of coefficients is unique for the spin-boson Hamiltonian studied, allowing one to calculate the time evolution from different initial states. To complement our numerical calculations, we apply the method to the Buck–Sukumar model. We find that when the ground-state energy of the model is unbounded and no ground state exists in a certain parameter space, the time evolution of the physical quantities is naturally unstable.     

Polarization of gamma-ray burst afterglows in the synchrotron self-Compton process from a highly relativistic jet

Linear polarization has been observed in both the prompt phase and afterglow of some bright gamma-ray bursts(GRBs).Polarization in the prompt phase spans a wide range,and may be as high as ■ 50%.In the afterglow phase,however,it is usually below 10%.According to the standard fireball model,GRBs are produced by synchrotron radiation and Compton scattering process in a highly relativistic jet ejected from the central engine.It is widely accepted that prompt emissions occur in the internal shock when shells with different velocities collide with each other,and the magnetic field advected by the jet from the central engine can be ordered on a large scale.On the other hand,afterglows are often assumed to occur in the external shock when the jet collides with interstellar medium,and the magnetic field produced by the shock through,for example,Weibel instability,is possibly random.In this paper,we calculate the polarization properties of the synchrotron self-Compton process from a highly relativistic jet,in which the magnetic field is randomly distributed in the shock plane.We also consider the generalized situation where a uniform magnetic component perpendicular to the shock plane is superposed on the random magnetic component.We show that it is difficult for the polarization to be larger than 10% if the seed electrons are isotropic in the jet frame.This may account for the observed upper limit of polarization in the afterglow phase of GRBs.In addition,if the random and uniform magnetic components decay with time at different speeds,then the polarization angle may change 90° during the temporal evolution.     

Coexistence of Two Mechanisms for Extracting Energy from a Rotating Black Hole

Evolution characteristics of a rotating black hole (BH) are discussed in coexistence of the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process in the parameter space consisting of the BH spin and the power-law index of the magnetic field on the disc. The condition for the coexistence of the two energy mechanisms are derived by using the mapping relation between the angular coordinate on the BH horizon and the radial coordinate on the disc. It is shown that not only the two mechanisms can coexist, but also the power and the rate of change of BH entropy in the BZ process will dominate over those in the MC process, provided that the BH spin and the power-law index are great enough.     

Order Parameter of a Nanometre-Scale S-Wave Superconducting Grain in Quantum Tunnelling Process： Frequency Space Analysis

A nano-scale s-wave superconducting grain, coupled to a normal metallic contact through a tunnelling junction, is placed in an external magnetic field. We suppose that effect of this quantum tunnelling on the Fourier transform of the order parameter is in the form of a small additive correction to the BCS order parameter. At the first order approximation in terms of this correction term and by using an instanton method, the related Green functions （in frequency space） are obtained. By establishing a self-consistent configuration an analytic formula for the order parameter is also found. We also show that a departure from superconductivity can be captured by this formula. This change of state is indeed a manifestation of a quantum transition induced by quantum fluctuations. In this sense, this is an advantage of our simple method which, like other more elaborate methods, can detect a quantum transition in the state of the grain.     

Connection of Screw Instability with Electric Current in an Accretion Disc around a Black Hole

The screw instability of the magnetic field is discussed based on its poloidal configuration generated by a single toroidal electric current flowing in the equatorial plane of a Kerr black hole （BH）. The rotation of the BH relative to the disc induces an electromotive force, which in turn results in a poloidal electric current. By using Ampere＇s law, we calculate the toroidal component of the magnetic field and derive a criterion for the screw instability of the magnetic field connecting the rotating BH with its surrounding disc. It is determined that the screw instability is related to two parameters： the radius of the disc and the BH spin. The occurrence of screw instability is depicted in a parameter space. In addition, we discuss the effect of the screw instability on magnetic extraction of energy from the rotating BH.     

Spontaneous emission from an atom in a photonic crystal with two coherent bands

The dynamic and the radiative properties of an excited three-level atom embedded in an anisotropic photonic crystal with two coherent bands are investigated.The relative position of the atom in a Wigner-Seitz cell is described with a position-dependent parameter θ(r0),which is used as the coherent parameter for the two bands.The result shows that the dynamic properties of the atomic system are not only determined by atomic transition frequencies,but also affected by the gap width and the coherence of the two bands.In addition,the spontaneous emission spectrum of the atomic transition in free space is discussed.The center and the intensity of the spectrum can be obviously manipulated via the coherent parameter.     

Growth-Parameter Spaces and Optical Properties of Cubic Boron Nitride Films on Si（001）

Cubic boron nitride （c-BN） films were deposited on Si（001） substrates in an ion beam assisted deposition （IBAD） system under various conditions, and the growth parameter spaces and optical properties of c-BN films have been investigated systematically. The results indicate that suitable ion bombardment is necessary for the growth of c-BN films, and a well defined parameter space can be established by using the P/a-parameter. The refractive index of BN films keeps a constant of 1.8 for the c-BN content lower than 50%, while for c-BN films with higher cubic phase the refractive index increases with the c-BN content from 1.8 at χc =50% to 2.1 at χc = 90%. Furthermore, the relationship between n and p for BN films can be described by the Anderson-Schreiber equation, and the overlap field parameter γ is determined to be 2.05.     

Probing Ho?ava-Lifshitz gravity using particle and photon dynamics in the presence of plasma

We study the particle motion around a black hole(BH) in Ho?ava-Lifshitz(HL) gravity with the Kehagias-Sfetsos(KS) parameter. First, the innermost stable circular orbit(ISCO) is obtained for massive particles around the BH in HL gravity. We find that the radii of the ISCOs decrease as the KS parameter decreases, meaning that the parameter ? causes the orbits of particles to move inward with respect to that of the Schwarzschild BH case.Then, the optical properties of a KS BH are studied in detail,...     

Prisoner's Dilemma on Co-Evolving Networks without Strategy Update

We investigate the game theory in a structured population with the assumption that the evolution of network structure is far faster than that of strategy update. We find that the degree distribution for the finM network consists of two distinct parts： the low degree part which is contributed to by defectors and a broadband in the regime with high degree which is formed by cooperators. The structure of the final network and the final strategy pattern have also been numerically proved to be independent of the game parameters.     

Dynamical properties of two-band superlattices with strong interband coupling in real space under the action of ac and dc－ac fields

Within a two-band tight-binding model driven by ac and dc－ac electric fields, using numerical methods, we investigate the dynamics of electrons and the quasi-energy spectrum of the system with strong interband coupling in real space. We find that when the bandwidth is suppressed to a value much smaller than the field frequency, the dynamical localization can exist in the system. The corresponding regions are found for the occurrence of dynamical localization in the parameter space.     

Comparison between the time-integrated spectrum and the peak time spectrum of gamma-ray bursts and possible implications

The mono-frequency peak luminosity and the corresponding photon energy of the time-integrated(Ls p,Es p)and peak time(Lt p,Et p)νfνspectra were derived for a sample of 38 redshift-known Fermi GRBs by fitting the spectra with the Band function.It was found that Et pis generally consistent with Es p,and Lt pis averagely three times larger than Ls p.The slope of the Lt p-Et prelation was consistent with that of the Ls p-Es prelation.The photon indices in the peak time spectrum,particularly,the index of the low energy end was,were statistically larger than that in the time-integrated spectrum.These results indicate that Ls pand Es pare dominated by Lt pand Et p,respectively.The difference of the spectral indices between the time-integrated and peak time spectra may be because of the overlap effect of a series of time-resolved spectra within a GRB.Our simulations,which were based on the observed spectral evolution and correlation between the energy flux and the peak energy within individual GRBs support our speculations.The Lt p-Et prelation may be less contaminated by the overlap effect,and it would may be an intrinsic feature of radiation physics.     

Initial Tests of a Rubidium Space Cold Atom Clock

We report the initial test results of a rubidium(~(87)Rb) space cold atom clock(SCAC).The space-qualified~(87)Rb SCAC is composed of the physical package,the optical bench,the microwave synthesizer and the control electronics.After the system is integrated,about 10~8 ~(87)Rb cold atoms are captured by magneto-optical trap.The linewidth of the Ramsey fringe is about 10 Hz for the free evolution time of 50 ms on the ground,and the signal-to-noise ratio is measured to be larger than 300.We demonstrate a good medium-term fractional frequency stability of 1.5 × 10~(-14) @1000s in the closed-loop operation on the ground.The main effects of the noise on the stability are also presented,and the optimized operating parameter is analyzed for the operation of SCAC in the microgravity environment.     

Gravitational quasi-normal modes of static R~2 Anti-de Sitter black holes

In this paper, we study the gravitational quasi-normal modes(QNMs) for a static R~2 black hole(BH) in Anti-de Sitter(AdS) spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R~2 AdS BH. The results show that the Re(ω) and |Im(ω)| of the QNMs increase together as |λ| increases for a given angular momentum number l. That indicates with a larger value of |λ| the corresponding R~2 AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R~2 BH might be helpful for the development of R~2 gravitational theory.     

A Lower Bound on the Entanglement in the Jaynes-Cummings Model

The entanglement between an atom and field is investigated by using the 3aynes-Cummings model. The initial atomic state is supposed in a mixed state and the field is in a squeezed state. The lower bound on the entanglement quantified by concurrence is calculated. It is found that the entanglement with the atom being initially in a mixed state can be larger than that with the atom being initially in a pure state. The entanglement is not a monotone function of the squeezing parameter r of the field and it achieves the maximum for certain r and then decreases with further increase of r.     

Entanglement in a two-qubit Heisenberg XXZ chain with different Dzyaloshinskii-Moriya couplings and an inhomogeneous magnetic field

Ground state entanglement and thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of the different Dzyaloshinski-Moriya interaction and inhomogeneous magnetic field are investigated.By the concept of concurrence,we find that the inhomogeneity of the magnetic field may make entanglement last for a long time and the critical temperature is dependent on Jz and b.The entanglement can be increased by increasing the temperature in some cases.We also find that the x-component parameter Dx has a higher critical temperature and more entanglement for a certain condition than the z-component parameter Dz.     

Topological Vortices in a Spin-Triplet Superconductor

Based on the complex three-component order parameter model of a spin-triplet superconductor, by using the C-mapping theory, we derive a new equation describing the distribution of the magnetic field for vortices, which can be reduced to the modified London equation in the case of ｜ψ^2｜^2 ~- ｜ψ^3｜^2 = 0 and Wl^1= 1. A magnetic flux quantization condition for vortices in a spin-triplet superconductor is also derived, which is topological-invariant. Fhrthermore, the branch processes during the evolution of the vortices in a spin-triplet superconductor are discussed. We also point out that the sum of the magnetic flux quantization that those vortices carried is 2nФo （Фo is the unit magnetic flux）, that is to say, the sum of winding number is even, which needs to be proved by experiment.     

Evolution of Ring Current Protons Induced by Electromagnetic Ion Cyclotron Waves

We investigate the evolution of the phase space density （PSD） of ring current protons induced by electromagnetic ion cyclotron （EMIC） waves at the location L=3.5, calculate the diffusion coefficients in pitch angle and momentum, and solve the standard two-dimensional Fokker-Planck diffusion equation. The pitch angle diffusion coefficient is found to be larger than the momentum diffusion coefficient by a factor of about 103 or above at lower pitch angles. We show that EMIC waves can produce efficient pitch angle scattering of energetic （- 100 keV） protons, yielding a rapid decrement in PSD, typically by a factor of - 10 within a few hours, consistent with observational data. This result further supports previous findings that wave-particle interaction is responsible for the rapid ring current decay.     

New approach for deriving the exact time evolution of the density operator for a diffusive anharmonic oscillator and its Wigner distribution function

Using thermal entangled state representation,we solve the master equation of a diffusive anharmonic oscillator(AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation.We present a new evolution formula of the Wigner function(WF) for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space.It is found that this formula is very convenient in investigating the WF’s evolution of any known initial state.As applications,this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.     

Detectivity of Fe Kα Lines in Gamma-Ray Bursts by Cerenkov Line Mechanism

The Fe Kα lines in gamma-ray bursts （GRBs） produced with the Cerenkov line mechanism are studied. We theoretically predict the Fe Kα line luminosities in both the early （before i hour） and late （～1 day） afterglows. Assuming about 200 GRBs could be detected by Swift per year, we sampled the redshift of these GRBs using the Monte Carlo method according to the GRB formation rate derived from the statistical correlation between the spectral peak energy and the peak luminosity of GRBs. Then we obtain the Fe Kα line flux distributions of the simulated GRB sample in the early and late phases. The simulated results show that the iron line flux is relatively low, so the line detection would be still a rare event at present. In addition, our results suggest that the iron lines from GRBs could be detected in the high redshift： z ～ 3 for the early phase and z ～ 6 for the late phase. Therefore, it is possible that the identification of Fe Ka lines in GRBs provides a tool to directly measure redshift and to study the high-redshift GRBs in the Swift era.