Gyrator transform of Gaussian beams with phase difference and generation of hollow beam

The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω₀. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.     

Supremum of the Airy2 Process Minus a Parabola on a Half Line

Let $\mathcal {A}_{2}(t)$ be the Airy₂ process. We show that the random variable $$\sup_{t\leq\alpha} \bigl\{\mathcal {A}_2(t)-t^2 \bigr\}+\min\{0,\alpha \}^2 $$ has the same distribution as the one-point marginal of the Airy_2→1 process at time α. These marginals form a family of distributions crossing over from the GUE Tracy-Widom distribution F _GUE(x) for the Gaussian Unitary Ensemble of random matrices, to a rescaled version of the GOE Tracy-Widom distribution F _GOE(4^1/3 x) for the Gaussian Orthogonal Ensemble. Furthermore, we show that for every α the distribution has the same right tail decay $e^{-\frac{4}{3} x^{3/2} }$ .     

First-Passage and Extreme-Value Statistics of a Particle Subject to a Constant Force Plus a Random Force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point x ₁ of a particle which starts at x ₀ with velocity v ₀. The probability that the particle has not yet arrived at x ₁ after a time t, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement m=max  _t [x(t)].     

Damping constant of Co/Pt multilayer thin-film media

Gilbert's damping constants, α, of Co(t_Co)/Pt (1.4 nm) multilayer thin films are investigated by Q-band FMR analysis. α is calculated from the resonance width of the FMR spectrum. With decreasing t_Co, the α value decreases from 0.034 (t_Co=8.7 nm) to 0.023 (t_Co=1.8 nm), and then increases to 0.037 (t_Co=1.0 nm). The decrease of α with t_Co>1.8 nm is probably due to the eddy current loss effects. The increase of α with t_Co<1.8 nm would be caused by the increase of the distortion between the Co and the Pt layers at the interface. When the magnetic field direction was changed from θ=90° (parallel to the specimen) to θ=0° (perpendicular to the specimen), the α of all the specimens increased, and a sharp step in α was observed around θ=40°, where the α has the maximum value.     

Detailed study of the effect of a short prepulse on soft X-ray spectra generated by a high-intensity KrF* laser pulse

The effect of a short prepulse (0.5 ps) on soft X-ray spectra from a plasma generated by a high intensity KrF* laser pulse (main pulse: 0.5 ps, intensity I _main=5.3×10¹⁵ W/cm²) on flat targets of Al and Cu has been studied in detail. The spectra have been measured as a function of the pulse separation t between the two pulses and the prepulse intensity I _pre. It was found that both the overall emission and the line emission increased with t (at constant I _pre) and with I _pre (at constant t). In particular, lines in the shorter wavelength region had higher intensity. The influence of the prepulse on the line emission of specific transitions in the Al spectra was investigated systematicly. An explanation for the observed effects is given.     

Dynamical theory for photon and photoelectric pulse distributions in single molecule fluorescence

A single two-level molecule driven by CW-laser field and a photomultiplier tube (PMT) are considered as two parts of the united dynamical system connected with each other by photons of molecular fluorescence. Each PMT is characterized by a rate α of photo-effect and by a rate β of PMT recovery. A theory for the photon distribution function w_N(t) and for the photoelectric pulse distribution function f_n(t) for such a system is built up. If times 1/ α and 1/ β characterizing PMT are much shorter as compared to the average time interval 1/ k between two successively emitted photons of fluorescence, the photon and the photoelectron distribution functions coincide with each other, i.e. f_n(t) ≅ w_N(t). A relation between w_N(t) and f_n(t) is studied in detail for the case in which PMT works slower as compared to the rate k of photon emission, i.e. at 1/ α, 1/ β ≥ 1/ k.     

Structure of Electromagnetic Fields in Crossed Gaussian Beams

Expressions for the fields of crossed Gaussian beams with foci shifted relative to the point of intersection of their axes are derived. It is shown that the linear corrections in parameter ε=1/kρ₀ must be taken into account in the crossed-beam intensity distribution (in contrast to the case of a single beam). The interference of crossed Gaussian beams has been investigated based on the intensity calculations taking into account linear corrections to the Poynting vector. The residual electron energy in crossed pulses is multiply increased in comparison with the case of acceleration in a single Gaussian pulse.     

The diffraction pattern of pp elastic scattering and the composite structure of the proton

The consequences of the quark-glue structure of hadrons for pp elastic scattering are examined in a simple model where the glue is taken to be the active constituent in normal (low p_T) hadronic collisions. Earlier work based on the study of pp inelastic diffraction led to the conclusion that the glue-glue elastic amplitude t_g is approximately Gaussian in the glue-glue impact parameter b_g, with maximum opacity at b_g = 0. A slight refinement of this approximation, in which t_g is almost maximally opaque over a small b_g interval and is Gaussian at larger b_g, is now shown to account for the remarkable diffraction structure observed in pp elastic scattering at ISR energies. A very simple form is obtained for the form factor describing the impact parameter distribution of the glue inside a proton relative to the proton itself.     

Creation of a sharper focus by using a rectified TEMp0 beam

The superresolution technique is usually used in optical imaging for its ability to make the central diffractive spot smaller than the Airy spot. In this paper, we apply the superresolution technique for transforming a symmetrical TEM_p0 Laguerre-Gauss beam into a Gaussian intensity distribution in the plane of a converging lens. The beam shaping is achieved by an annular binary Diffractive Optical Element having a transmittance, alternatively equal to −1 or + 1, modelled on the p light rings of the incident beam. It is observed that the rectified TEM₃₀ beam at focus has a focal volume 170 times smaller than that of a Gaussian beam.     

Functional integral representations of partition function without limiting procedure. Techniques of calculation of moments

A definition of the Feynman path integral which does not rest on a limiting procedure based on time-slicing has been given by DeWitt-Morette. We present in this paper a discussion of real Gaussian measures and formulate expressions for the quantum statistical partition function directly in terms of measures of integration on the topological vector space ø₀ of continuous functions defined on the time intervalT = (t _a ,t _b ), such thatx(t _a ,t _b )=0 for allx ? ø₀. We give a definition of a measure for the space ø₀ equivalent to the path integral based on the Uhlenbeck-Ornstein probability distribution. We give expressions for the partition function using the Wiener-Feynman measure and the Uhlenbeck-Ornstein measure. As an exercise in the use of the new techniques, we present calculations of moments of potential functions. The techniques will enable one to solve in a rigorous manner practical problems in quantum statistical mechanics.     

α-碘酸锂的电流弛豫和偏压场作用下表观介电常数弛豫行为

本工作较为详细地测定了静电场作用下α-碘酸锂的电流弛豫行为:在撤去c轴方向上的静电场后,从我们所用测量电流仪器的响应时间到某一t_k的区间内,放电电流服从(t/t₀)^-α的负幂次方律;而在t>t_k,其规律近似地为:(t/t₀)^{(-α′ln(t/t₀))}。相关的弛豫参数α,α′和t_k在有限的范围内,依赖于温度和施加电压的大小,也因样品不同而有差异。对将近十个样品进行了测试,结果表明,大多数晶体在尽可能小的电压下0.43≤α≤0.7,0.07<α′<0.09;上述的电流弛豫表达式与α-碘酸锂在偏压场作用下观察到的其它物理现象的弛豫行为,与在中子衍射加强和表观介电常数中的表现如出一辙;可以初步肯定各种现象的弛豫行为具有相同的物理根源。 关键词：     

Approximate analytical expressions of apertured broadband beams in the far field

The approximate analytical expressions of the apertured broadband beams in the far field with Gaussian and Laguerre-Gaussian spatial modes are presented.For the radially polarized Laguerre-Gaussian beam,the result reveals that the electromagnetic field in the far field is transverse magnetic.The influences of bandwidth(Γ) and truncation parameter(C 0) on the transverse intensity distribution of the Gaussian beam and on the energy flux distribution of radially polarized Laguerre-Gaussian beam are analysed.     

A measurement of the KL0p → KS0p reaction between 4 and 14 GeV/c in the range 0.1 ⩽|t|⩽ 2 GeV2

We present experimental data on the K_L⁰p → K_S⁰p reaction between 4 and 14 GeV/c in the range 0.1 ? |t| ? 2 GeV². This experiment has been performed at the CERN PS, using spark chambers and a large aperture magnet. The results show a break of slope at t = ?0.3 GeV². The ω trajectory deduced from the data has an intercept α(0) = 0.5 and a slope α′ = 0.88. A comparison with various models shows that the non-flip amplitude is dominant.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

First and second order ferromagnetic transition at in a 1D itinerant system

We consider a modified version of the one-dimensional Hubbard model, the t ₁ - t ₂ Hubbard chain, which includes an additional next-nearest-neighbor hopping. It has been shown that at weak coupling this model has a Luttinger liquid phase or a spin liquid phase depending upon the ratio of t₂ to t₁. Additionally if the on-site interaction U is large enough, the ground state is fully polarized. Using exact diagonalization and the density-matrix renormalization group, we show that the transition to the ferromagnetic phase is either of first or second order depending on whether the Luttinger liquid or spin liquid is being destabilized. Since we work at T =0, the second order transition is a quantum magnetic critical point. Received 21 July 1999     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

Bead-spring model of a polymer chain: A transient solution

With the Rouse-Zimm differential equation of the spring-bead model, the distribution function ofN + 1 beads(x, y, z,t) [here x denotes x₀, x₁,..., x_N, and similarly for y and z] is explicitly solved with the two different initial conditions: the Gaussian and delta distribution functions. We find that although the mean end-to-end distances obtained from the two initial conditions are the same, the expressions of the mean square end-to-end distances are different. We also obtain the expression for the mean and mean square end-to-end distances analytically from the Langevin equation with the delta initial distribution function. With this analytic expression, we show that the statistical quantities obtained from the Monte Carlo calculation are consistent with those obtained from the Rouse-Zimm differential equation if a suitable length is chosen for the time increment.NIH-Special Fellow (1F03GM43885-01) with a partial support by USPHS GM11916.     

The reactions N14(n, α)B11 and N14(n,t)C12 observed with a gridded ionization chamber

The cross sections for the reactions N¹⁴(n, α)B¹¹ and N¹⁴(n, t)C¹² have been measured in the neutron energy range 4.0 to 6.4 MeV and at 2.5 MeV. Mono-energetic neutrons were produced in the D(d, n) He³ reaction using a gas target. The (n, α) and (n, t) disintegrations were detected in a gridded ionization chamber filled with an argonnitrogen mixture. The response of the chamber under different operation conditions is described. The excitation functions, measured with a neutron energy resolution of 40 to 50 keV, are given for theα ₀ group from the N¹⁴(n,α)B¹¹ reaction over the entire neutron energy range and for theα ₁ group and the t₀ group from N¹⁴(n, t) C¹² for neutron energies above 4.3 and 5.6 MeV, respectively.     

KdV-soliton dynamics in a random field

We consider the interaction between soliton and a spatially uniform external random field within the framework of the forced Korteweg-de Vries equation. In the general case, the averaged soliton field is transformed to a Gaussian pulse whose amplitude falls off with time as t^−α, while its width increases as t^α, where the parameter α is characterized by the statistical properties of the external force. We obtain an analytical solution for α = 2, which corresponds to the limiting case of an infinitely long correlation time (τ₀ → ∞). The obtained solution is compared with the well-known Wadati solution for the case of a delta-correlated external force (τ₀ → 0) where the soliton is transformed to a Gaussian pulse with amplitude falling off at a lower rate α = 3/2. The numerical solutions of the forced Korteweg-de Vries equation, which demonstrate an increase in the parameter α from 3/2 to 2 with increasing correlation time, are given for the intermediate case corresponding to 0 < τ₀ < ∞. It is shown that the amplitude of the averaged soliton in a periodic random field falls off as t⁻¹ for the long times t. In this case, two pulses propagating in different directions are formed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 599–606, July 2006.     

On the asymptotical normality of statistical solutions for harmonic crystals in half-space

We consider the dynamics of a harmonic crystal in the half-space with zero boundary condition. It is assumed that the initial date is a random function with zero-mean, finite-mean energy density which also satisfies a mixing condition of Rosenblatt or Ibragimov type. We study the distribution μ _t of the solution at time t ∈ ℝ. The main result is the convergence of μ _t as t → ∞ to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian in general). Supported partly by research grant of RFBR (06-01-00096).