Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State

We find a new x-parameter squeezed coherent state （p, q）κ representation, which possesses well-behaved features, i.e., its Wigner function＇s marginal distribution in the ＂q-direction＂ and in the ＂p-direction＂ is the Gauss/an form exp（-κ（q＇ - q）2}, and exp{（p＇ - p）2/κ}, respectively. Based on this, the Husimi function of（p, q）κ is also obtained, which is a Gauss/an broaden version of the Wigner function. The （P, q）κ state provides a good representative space for studying various properties ot the Husimi operator.     

Distribution Function of Mesoscopic Hopping Conductance

We study mesoscopic hopping conductance by computer simulation distribution functions(DFs),It is found that the distributions obtained by choosing randomly the chemical potentials(for a fixed impurity configuration),which corresponds to a typical experimental situation,coincide with those obtained when both impurity configuration and chemical potential are chosen randmly,in agreement with the ergodicity hypothesis.The DFs in shape obtained for one-dimensional system are found to be quite close to the predictions of the theory by Raikh and Ruzin.For the two-dimensional case,the DFs both for a narrow system and thin film look to be similar(and close to the one-dimensional case).The DF for the conductance of the square sample is nearly Gaussian.     

Is the Cabibbo Angle a Function of the Weinberg Mixing Parameter?

The (u, c) quarks and (d, s) quarks arerequired to have mass matrices of a certainform. To achieve these mass matrices appropriate Lagrangians are assumed. Theu quark is coupled to the standard Higgs scalar _L. Thec quark has a ₅ couplingwith _L and _R, where _R is the Higgs scalar corresponding to theleft-rightmodel. The u quark has no ₅ coupling. Both u,c quarks have a Yukawa couplingwith a Higgs multiplet. Exactly similar Lagrangians are chosen for thed, s qurks.Using these mass matrices, the Cabibbo angle is found to be 13° 11. The ratiom _c/m _s is shown to be approximately 3.1 with the help of the Weinberg mixingparameter. The mixing angles ₂ and ₁ determine the Cabibbo angle. The ratiotan ₂/ tan ₁ is shown to be a function of the Weinberg mixing parameter.     

Spatial Characteristics of Head-Related Transfer Function

The spatial characteristics of head-related transfer functions (HRTFs) are studied by a spatial Fourier analysis.A law of the HRTF spatial sampling in different elevation planes is obtained, and the corresponding spatial interpolating method used to recover the continuous HRTF is proposed. The method is valid, for the average error between the measured and interpolated HRTFs in the horizontal plane is about 0.5%. These results provide guidance for the discrete spatial measurement of HRTFs.     

Autocorrelation Function of Hydrogen Atoms in Magnetic Fields

The autocorrelation function is an important quantity that can reflect the dynamical properties of the Rydberg wave packet and can be measured in experiments. Applying time-dependent perturbation theory and rotating wave approximation, we derive the autocorrelation function of the double-pulse laser describing the evolution of a Rydberg wave packet of hydrogen atoms in magnetic fields. The resulting expression is written as a sum of the modified Caussian terms. Each Caussian term comes from a parent semiclassical closed orbit. It provides a direct explanation and experimentally controllable measurement scheme, which allows us therefore to recognize the closed orbit and to determine its returning time in high precision.     

Direct Measurement of the Correlation Function of Optical–Terahertz Biphotons

JETP Letters - The second-order correlation function which characterizes the quantum correlation between the optical and terahertz photons generated under spontaneous parametric down-conversion has...     

Calculation of the Longitudinal Structure Function from Regge-Like Behaviour of the Gluon Distribution Function in Leading Order Approximation at Low x

We present the calculations of FL longitudinal structure functions from DGLAP evolution equation in leading order （LO） at low-x, assuming the Regge-like behaviour of gluon distribution at this limit. The calculated results are compared with the H1 data and QCD fit. It is shown that the obtained results are very close to the mentioned methods. The proposed simple analytical relation for EL provides a t-evolution equation for the determination of the longitudinal structure function at low-x. All the results can consistently be described within the framework of perturbative QCD, which essentially shows increases as x decreases.     

Three Kinds of Velocity Structure Function in Turbulent Flows

Based on the local multi-scale eddy structures in turbulent flows, we elucidate the essential difference between the real turbulent field with a finite Reynolds number and the Kolmogorov fully developed random field. The motion of fluid particles in the real turbulent field is not fully random. There exist multi-scale structures due to the effect of viscosity. Actually the movements of fluid particles in the turbulent field are restricted by such eddy structures. Furthermore, concept of the locally averaged velocity structure function is put forward to describe the relative strain distortion of two adjacent turbulent eddy structures at a certain scale. The time sequence of the longitudinal velocity component at different vertical locations in turbulent boundary layer has been elaborately measured by the constant temperature anemometry of model 1FA-300 in a wind tunnel. The experiment proves that the locally averaged velocity structure function is in agreement with the wavelet-coefficient structure function.     

Form of Scaling Function in Quantum Hall Plateau Transitions

We have measured the temperature dependence of the resistance Rxx and Rxy of a two-dimensional electron system in the regime of the quantum Hall plateau transition. We observe for our sample a considerable large critical exponent κ～ 0.66 - 0.77, which may be due to the dominant electron-phonon scattering. Further we find a simple exponential form of Rxx = Rc exp（-s） in agreement with the theoretically proposed universal scaling function.     

Recovery of Graded Index Profile of Planar Waveguide by Cubic Spline Function

A method is proposed to recover the refractive index profile of graded waveguide from the effective indices by a cubic spline interpolation function. Numerical analysis of several typical index distributions show that the refractive index profile can be reconstructed closely to its exact profile by the presented interpolation model.     

Effect of the Initial Mass Function of Primaries on Binary Stellar Populations

Using evolutionary population synthesis technique, we explore the behaviour of the integrated U-B,B-V, V-R and R - I colours, the integrated spectral energy- distributions (ISEDs) and Lick/IDS absorption-line indices of instantaneous burst solar-metallicity binary stellar populations, as a function of the initial mass function (IMF)of primaries. It is found that the variation of the IMF of primaries produces a small effect on the integrated colours and the Lick/IDS indices, while a significant difference in the absolute ISEDs.     

Is It Possible to Study the Wave Function of 2S Vector Mesons at HERA?

We present a short review of anomalous properties in diffractive photo- and electroproduction of radially excited V(2S) vector mesons. Using the color dipole generalized Balitsky-Fadin-Kuraev-Lipatov phenomenology we analyze anomalous Q ² and energy dependence of the production cross section, V(2S)/V(1S) production ratio, the diffraction slope and anomalous t-behavior of the differential cross section d/dt. The origin of these anomalies is based on the interplay of the nodal structure of V(2S) radial wave function with the energy and dipole size dependence of the dipole cross section and the diffraction slope. We analyze how a different pattern of anomalous behavior of V(2S) production leads to a different position of the node in the wave function and discuss how that node position can be extracted from the data at HERA.     

Is the Collecting Surface of a Flat One-Sided Probe Constant when Measuring the Ion Distribution Function?

The correctness of the known plane single-ended probe method for measuring the anisotropic ion distribution functions in a gas-discharge plasma has been considered. Analysis has been performed for positive probe potentials relative to the plasma with magnitudes on the order of the mean ion energy, which as a rule is much lower than the mean electron energy. We have analyzed the dependence of the collection surface area of a plane probe on its potential in this range. The structure of the near-probe layer has been determined for an isotropic electron distribution function of the Maxwellian or Druvestein type and an anisotropic ion distribution function. These results are used to derive analytic relations for the correction to the second derivative of the probe current with respect to the plane probe potential. It has been shown that, when the ion distribution function is measured in a wide range of conditions in the gas-discharge plasma, when the approximation of a collisionless probe layer is applicable, and the probe does not perturb the plasma, the dependence of the collection surface area of the probe on the potential can be disregarded in this range.     

Stellar Mass Function of Lyman Break Galaxies： Theoretical Perspective

Adopting the observational distributions of star formation rates and half-light radii of Lyman break galaxies （LBGs） in the rest frame UV, we investigate empirically the predicted stellar mass function for LBGs. It is found that a peak exists at mass around 1.5 × 10^10M⊙ for their stellar mass function and there have been significant amount of LBGs with stellar masses higher than 10^11M⊙ at z ～ 3. There should be two families for LBG population observed by the Infrared Array Camera （IRAC） （which is a key instrument in the infrared space telescope Spitzer）, one is red and the other is blue, which are consistent with recent works. Moreover, the predicted comoving correlation lengths for LBGs with different stellar masses, i.e., with different 8 μm magnitudes, are also discussed. The red LBGs should be clustered in space more strongly than the blue LBGs. These predictions can and will be tested by the observations of IRAC, and will provide strong constraints on the current hierarchical galaxy formation model.     

Energy Dependence of String Fragmentation Function and φ Meson Production

The φ meson productions in Au+Au and/or Pb+Pb collisions at AGS, SPS, RHIC, and LHC energies have been studied systematically with a hadron and string cascade model LUCIAE. After considering the energy dependence of the model parameter α in string fragmentation function and adjusting it to the experimental data of charged multiplicity to a certain extent, the model predictions for φ meson yield, rapidity, and transverse mass distributions are compatible with the experimental data at AGS, SPS and RHIC energies. A calculation for Pb+Pb collisions at LHC energy is given as well. The obtained fractional variable in string fragmentation function shows a saturation in energy dependence. It is discussed that the saturation of fractional variable in string fragmentation function might be a qualitative representation of the energy dependence of nuclear transparency.     

Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function

The Tracy-Widom distribution functions involve integrals of a Painlevé II function starting from positive infinity. In this paper, we express the Tracy-Widom distribution functions in terms of integrals starting from minus infinity. There are two consequences of these new representations. The first is the evaluation of the total integral of the Hastings-McLeod solution of the Painlevé II equation. The second is the evaluation of the constant term of the asymptotic expansions of the Tracy-Widom distribution functions as the distribution parameter approaches minus infinity. For the GUE Tracy-Widom distribution function, this gives an alternative proof of the recent work of Deift, Its, and Krasovsky. The constant terms for the GOE and GSE Tracy-Widom distribution functions are new.     

Rotational Invariance of the 2d Spin – Spin Correlation Function

At the critical temperature in the 2d Ising model on the square lattice, we establish the rotational invariance of the spin-spin correlation function using the asymptotics of the spin-spin correlation function along special directions (McCoy and Wu in the two dimensional Ising model. Harvard University Press, Cambridge, 1973) and the finite difference Hirota equation for which the spin-spin correlation function is shown to satisfy (Perk in Phys Lett A 79:3–5, 1980; Perk in Proceedings of III international symposium on selected topics in statistical mechanics, Dubna, August 22–26, 1984, JINR, vol II, pp 138–151, 1985).     

Transformation Formula of the “Second” Order Mock Theta Function

We give a transformation formula for the “second order” mock theta function

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅱ

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations.     

Scheme for Direct Measurement of Wigner Characteristic Function for Motion of a Single Trapped Ion

In this paper, a procedure is proposed for measuring Wigner characteristic function for motion of a single trapped ion. In the scheme, the trapped ion is driven by two laser beams with different frequencies tuned to the first lower and upper vibrational sidebands, respectively. Unlike other previous scheme, our scheme does not require the displacement of the external state before the ion-laser interaction and thus our scheme night be more simple and feasible. The scheme can also be used to prepare the motional Schroedinger cat states and entangled coherent states.