Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formalism of the Dirac equation with a generalized Hylleraas potential of the form V(r) = V0(a+exp(λr))/(b+ exp(λr)) + V1(d+exp(λr))/(b+exp(λr)).We obtain the bound state energy eigenvalue and the corresponding eigenfunction expressed in terms of the Jacobi polynomials.By choosing appropriate parameter in the potential model,the generalized Hylleraas potential reduces to the well known potentials as special cases.     

Bound states of the Klein－Gordon and Dirac equations for potential V0tanh2(r/d)

The exact bound state wavefunctions and energy equations of Klein－Gordon and Dirac equations are given with equal scalar and vector potential s(r)=v(r)=V(r)/2=V_0tanh^2(r/d). The relation between the energy equation and that of relativistic harmonic is discussed.     

Continuous generation of dissipative spatial solitons in two-dimensional Ginzburg–Landau models with elliptical shaped potentials

We report on the rich dynamics of two-dimensional fundamental solitons coupled and interacting on the top of an elliptical shaped potential in a two-dimensional Ginzburg–Landau model. Under the elliptical shaped potential, the solitons display unique and dynamic properties, such as the generation of straight-line arrays, emission of either one elliptical shaped soliton or several elliptical ring soliton arrays, and soliton decay. When changing the depth and sharpness of the external potential and fixing other parameters of the potential, various scenarios of soliton dynamics are also revealed. These results suggest some possible applications for all-optical data-processing schemes, such as the routing of light signals in optical communication devices.     

Spin-dependent transport through an interacting quantum dot system

Using an equation of motion technique, we report on a theoretical analysis of transport characteristics of a spin-valve system formed by a quantum dot coupled to ferromagnetic leads, whose magnetic moments are oriented at an angle θ with respect to each other, and a mesoscopic ring by the Anderson Hamiltonian. We analyse the density of states of this system, and our results reveal that the density of states show some noticeable characteristics depending on the relative angle θ of magnetic moment M, and the spin-polarised strength P in ferromagnetic leads, and also the magnetic flux Φ and the number of lattice sites N_R in the mesoscopic ring. These effects might have some potential applications in spintronics.     

Effect of isotope on state-to-state dynamics for reactive collision reactions ■ and ■ in ground state 1~2 A’’ and first excited 1~2 A’ potential energy surfaces

We carry out quantum scattering dynamics and quasi-classical trajectory(QCT) calculations for the O+H_2~+ reactive collision in the ground(1~2 A").nd first excited(1~2 A') potential energy surface.We calculate the reaction probabilities of O+H_2~+(v=0,j=0)→OH~++H and O+H_2~+(v=0,j=0)→OH+H~+reaction for total angular momentum J=0.The results calculated by QCT are consistent with those from quantum mechanical wave packet.Using the QCT method,we generate in the center-of-mass frame the product state-resolved integral cross-sections(ICSs);two commonly used generalized polarization-dependent differential cross-sections(PDDCS s),(2π/σ)(dσ_(00)/dω_t),(2π/σ)(dσ_(20)/dω_t));and three angular distributions of the product rotational vectors,p(θ_r),P(φ_r),and p(θ_r,φ_r).We discuss the influence on the scalar and vector properties of the potential energy surface,the collision energy,and the isotope mass.Since there are deep potential wells in these two potential energy surfaces,their kinetic characteristics are similar to each other and the isotopic effect is not obvious.However,the well depths and configurations of the two potential energy surfaces are different,so the effects of isotopic substitution on the integral cross-section and the rotational polarization of product are different.     

Two-Dimensional Rayleigh-Taylor Instability in Incompressible Fluids at Arbitrary Atwood Numbers

The Rayleigh-Taylor instability in two-dimensional incompressible fluids at arbitrary Atwood numbers is studied by expanding the perturbation velocity potential to third order. The second and third harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The mode coupling coefficients are dependent on the Atwood numbers. Our simulations support the weakly nonlinear results. We find that the ratio of the nonlinear saturation amplitude ηs and the perturbation wavelength λ is dependent on the Atwood number AT and the relation is ηs/λ=（1/π）[√2/5/√（1＋3AT2 ）].     

Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

We intend to realize the step-up and step-down operators of the potential V (x) = V1 e 2βx+V2 e βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β→β).     

Attosecond manipulation of ionization and efficient broadband supercontinuum generation in stretched molecules

<正>We theoretically investigate the high-order harmonic generation from stretched molecules in a linearly polarized intense field.By adopting an infrared pulse combined with an ultraviolet(UV) attosecond pulse,the ionization process can be controlled effectively.In this excitation scheme,the harmonic spectrum beyond I_p+3.17U_P is significantly enhanced by two orders,where I_p and U_p=e~2E_0~2/(4m_eω~2) are the ionization and ponderomotive potential,then smooth broadband supercontinuum with the bandwidth of about 120 eV is obtained,which leads to an isolated sub-60- as attosecond pulse with a high signal-noise ratio.Moreover,the bandwidth of the supercontinuum is weakly dependent on the location and pulse duration of the UV pulse.     

Stereodynamics of the reactions: F+H_2/HD/HT→FH+H/D/T

Among many kinds of ways to study the properties of atom and molecule collision, the quasi-classical trajectory(QCT) method is an effective one to investigate the molecular reaction dynamics. QCT calculations have been carried out to investigate the stereodynamics of the reactions F + H2/HD/HT→FH + H/D/T, which proceed on the lowest-lying electronic states of the FH2 system based on the potential energy surface(PES) of the 12A' FH2 ground state. Although the QCT method cannot describe all quantum effects in the process of the reaction, it has unique advantages when facing a three-atoms system or complicated polyatomic systems. Differential cross sections(DCSs) and three angle distribution functions P(θr), P(φr), P(θr, φr) on the PES at the collision of 2.74 kcal/mol have been investigated. The isotope effect becomes more obvious with the reagent molecule H2 turning into HD and HT. P(θr, φr), as the joint probability density function of both polar angles θr and φr, can reflect the properties of three-dimensional dynamic more intuitively.     

A feasible method for comparing the power dependent photostability of fluorescent proteins

A feasible method of combining the concept of fluorescence half-life and the power dependent photo- bleaching rate for characterizing the practical photostability of fluorescent proteins(FPs)was introduced. Furthermore,by using a fluorescent photostability standard,a relative comparison of the photostabilty of FPs from different research groups was proposed,which would be of great benefit for developing novel FPs with optimized emission wavelength,better brightness,and improved photostability.We used rho- damine B as an example to verify this method and evaluate the practical photostability of a far-red FP, mKate-S158C.Experimental results indicated good potential of this method for further study.     

A light scalar in the Minimal Dilaton Model in light of the LHC constraints

Whether an additional light scalar exists is an interesting topic in particle physics beyond the Standard Model(SM), as we do not know as yet the nature of physics beyond the SM in the low mass region in view of the inconsistent results of the ATLAS and CMS collaborations in their search for light resonances around 95 GeV in the diphoton channel. We study a light scalar in the Minimal Dilaton Model(MDM). Under the theoretical and the latest experimental constraints, we sort the selected data samples into two scenarios according to the diphoton rate of the light scalar: the large-diphoton scenario(with σ_(γγ)/SM■0.2) and the small-diphoton scenario(with σ_(γγ)/SM■0.2),which are favored by the CMS and ATLAS results, respectively. We compare the two scenarios, test the characteristics of the model parameters, the scalar couplings, production and decay, and consider how they could be further discerned at colliders. We draw the following conclusions for the two scenarios:(i) The large-diphoton scenario has in general a small Higgs-dilaton mixing angle(|sinθ_S|■0.2) and a small dilaton vacuum expectation value(VEV)f(0.5■η≡ v/f■1),and the small-diphoton scenario has large mixing(| sinθ_S|■0.4) or large VEV(η≡v/f ■0.3).(ii) The large-diphoton scenario in general predicts small syy coupling(|C_(sγγ)/SM|■ 0.3) and large sgg coupling(0.6■|C_(sgg)/SM|■1.2), while the small-diphoton scenario predicts small sgg coupling(|C_(sgg)/SM|■0.5).(iii) The large-diphoton scenario can interpret the small diphoton excess seen by CMS at its central value, when m_s■ 95 GeV,η■0.6 and | sinθ_S|■0.(iv) The large-diphoton scenario in general predicts a negative correlation between the Higgs couplings |C_(hγγ)/SMI and |C_(hgg)/SM|, while the small-diphoton scenario predicts that both couplings are smaller than 1,or |C_(hγγ)/SM|■0.9■|C_(hgg)/SM|.     

Simple optical method for small angular displacement measurement based on the astigmatic effect

We propose a novel small-angle measuring optical method based on the astigmatic effect of two orthogonally placed cylindrical lenses. According to the one-to-one correspondence between the laser spot shape and the angle,the angle is determined. We theoretically analyze the measuring range and demonstrate that a longer distance between the rotating axis and the optical axis leads to a smaller measuring range, but better sensitivity. Also, an associated experimental system is established and a measuring range of 0.94 mrad(cubic fit r = 0.9993) as well as a good linear range of 0.37 mrad(linear fit r=0.9994) with a resolution of 8 μrad is achieved.     

Inflation model selection revisited

We update the constraints on the power spectra of primordial curvature perturbation and tensor perturbation including Planck data 2015(P15) and recently released BICEP2/Keck data(BK15), Baryon Acoustic Oscillation data and the Type Ia supernovae data.We find that the upper limits of tensor-to-scalar ratio are 0.061, 0.064 and 0.072 at 95% confidence level(CL) in the ΛCDM+r,ΛCDM+r+α_s and ΛCDM+r+α_s+β_s models respectively, where αsand βsare the running of scalar spectral index and running of running. The inflation model with a concave potential is favored at more than 95% CL. In addition, parametrizing the slow-roll parameter ? ～ 1/N~p, where N is the e-folding number before the end of inflation and taken in the range of [50, 60] and [14, 75]respectively, we conclude that the inflation model with a monomial potential V(?) ～ ?~n is disfavored at more than 95% CL, and both the Starobinsky inflation model and brane inflation model are still consistent with the data.     

Solution of the Dirac Equation for Ring-Shaped Modified Kratzer Potential

We propose a new exactly solvable potential which is formed by modified Kratzer potential plus a new ring-shaped potential η cot2θ/r2. The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.     

Theoretical study of stereodynamics for the reaction O（3P）+D2（v= 0,j=0） → OD+D and isotope effect

Quasi-classical trajectory (QCT) calculations have been performed to study the product polarization behaviours in the reaction O(3P) + D2 (v = 0, j = 0) → OD + D. By running trajectories on the 3A and 3A potential energy surfaces (PESs), vector correlations such as the distributions of the polarization-dependent differential cross sections (PDDCSs), the angular distributions of P (θr) and P (φr) are presented. Isotope effect is discussed in this work by a comprehensive comparison with the reaction O(3P) + H2 (v = 0, j = 0) → H + H. Common characteristics as well as differences are discussed in product alignment and orientation for the two reactions. The isotope mass effect differs on the two potential energy surfaces: the isotope mass effect has stronger influence on P (θr) and PDDCSs of the 3A PES while the opposite on P (φr) of the 3A potential energy surface.     

Effect of Anisotropic Impurity Scattering in D-Wave Superconductors

In d_x²-y²-wave superconductors,the effect of s-wave point disorder has been extensively studied in literature.We study the anisotropic disorder in the form of V_kk’^imp=V_if_kf_k’ with f_k=cos(2θ)(θ the azimuthal angle of k),as proposed to be caused by apical oxygen vacancies in overdoped La-based cuprate films,under the Born approximation.The disorder self-energy and d-wave pairing affect each other and...     

New Exact Solutions and Dynamics in （3＋1）-Dimensional Gross-Pitaevskii Equation with Repulsive Harmonic Potential

Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the （3＋1）-dimensional Gross-Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.     

High-intensity molecular harmonic generation without ionization

We theoretically investigate high-order harmonic generation from H + 2 in an infrared laser field.Our numerical simulations show that a highly efficient plateau structure exists in the molecular harmonic spectrum.Under the action of the infrared laser pulse,the bound electronic wave packet in a potential well has enough time to tunnel through the effective potential barrier,which is formed by the molecular potential and the infrared laser field,and then recombine with the neighboring nucleus emitting a harmonic photon.During the entire dynamic process,because the wave packet is mainly located in the effective potential,the diffusion effect is of no significance,and thus a highly efficient harmonic plateau can be achieved.Specifically,the cut-off frequency of the plateau is linearly scaled with the peak amplitude of the infrared laser electric field,which may open another route to examine the internuclear distance of the molecule.Furthermore,one may detect the molecular bond lengths using the harmonic plateau.     

Rotating soliton clusters in nonlocal nonlinear media

From the study of the dynamics for the ring-like soliton clusters, we find that there exists a critical value of the ring radius, dcr, for the stationary rotation of the clusters with respect to the beam centre even in the presence of the relatively strong noise, and that the soliton clusters will not rotate but only undergo periodic collisions in the form of simple harmonic oscillator if the ring radius is large enough. We also show that the direction of the rotation can be opposite to the direction of phase gradient when the relative phase difference is within the domain 0 〈 ｜θ｜ 〈 π, while along the direction of phase gradient when the relative phase difference is within the domain π 〈｜θ｜ 〈 2π     

Valence orbital method of calculating harmonic emission from diatomic molecule

We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital on harmonic emissions from N₂ and O₂ molecules in detail separately. The calculation results confirm the different properties of harmonic yields from N₂ and O₂ molecules which are well consistent with available experimental data. We observe that due to the orientation dependence of \sigma and \pi orbitals, the bonding orbital (\sigma _{2pz} )^2 of N₂ determines the maximum of harmonic emission when the molecular axis of N₂ is aligned parallel to the laser vector, and the magnitude of the high harmonic signal gradually weakens with the orientation angle of molecular axis increasing. But for O₂ molecule the antibonding orbitals (\pi _{2py}^\ast )^1 and (\pi _{2pz}^\ast )^1 contribute to the maximum of harmonic yield when O₂ is aligned at 45^{\circ} and bonding orbitals (\pi _{2py} )^2 and (\pi _{2pz} )^2 slightly influence the orientation angle of maximum of harmonic radiation not exactly at 45^{\circ}.