Photon-echo decay due to weak velocity-changing collisions

Using statistical arguments, we derive an exact expression (valid for any collision kernel) for the decay of a two-pulse photon echo in the limit in which the decay occurs as the result of “weak” (glancing) velocity-changing collisions.     

Time-resolved saturated-absorption experiment. Effect of velocity-changing collisions upon non-thermal-equilibrium atomic velocities

Results obtained in a time-resolved study of atomic-velocities thermalization for the ¹D₂ metastable level of the barium transition 6 ¹P₁ → 5 ¹D₂ are presented. Time evolution of the absorption coefficient after saturation due to a strong monochromatic laser pulse is studied. The results are analyzed in the strong-collision model, including trapping effects in the ¹P₁ level. For barium and rare-gas mixtures the cross sections for strong elastic collisions are in agreement with the cross sections deduced from the kinetic theory.     

Experimental study on methods minimizing the influence of velocity-changing collisions in Doppler-free saturation spectroscopy

A method based on homodyne mixing is described which facilitates the use of rf-modulation of the pump beam for laser saturation spectroscopy together with conventional kHz lock-in amplifiers yielding a substantial reduction of disturbing pedestals present due to collisions in an atomic vapour. The technique benefits also from the significant improvement in the signal to noise ratio when transferring the Doppler-free signal to a frequency domain of several MHz where the interfering laser noise is low. These experimental procedures allow measurements of high quality saturated absorption spectra in vapour cells of otherwise unfavourable high gas pressure such as in commercial see-through hollow-cathodes. In addition we report the detection of an optogalvanic signal at rf-modulation (3.3 MHz).     

Cusp and Regular Ion-Acoustic Solitons

Cups and regular smooth solitons are studied using the fluid model in cylindrical geometry for parallel propagating ion-acoustic waves in a low β plasma. It is found that smooth solitons only occur in the supersonic regime, whereas cusp solitons occur both in supersonic and subsonic regimes. In the supersonic regime, the amplitude and the width of cusp solitons increase when the Mach number M increases and initial electric field E ₀ decreases. However, the amplitude of smooth regular solitons increases and their width decreases when E ₀ increases and M decreases. For the subsonic case, both the amplitude as well as the width of a cusp solitons increase when M increases and E ₀ decreases. Corresponding to these cusp and regular solitons, bipolar electric field structures are also studied. These results may be helpful in understanding the properties of ion-acoustic regular and cusp solitons in space plasmas.     

Cusp catastrophe in slowly varying equilibriums

Solutions of the equations v _x+v ³?tv+x=0 and v _xx=v ³? tv+x, which describe the nucleation of domain walls occurring in the neighborhood of cusps of slowly varying equilibriums, are analyzed. Examples related to the diffusion in smoothly inhomogeneous media are considered.     

Cusp Singularities in Boundary-Driven Diffusive Systems

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities. The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.     

二次谐波回旋行波管Cusp电子枪的模拟与实验研究

利用3D PIC软件和乌克兰开发的电子光学计算软件TAU对二次谐波回旋行波管Cusp电子枪进行模拟,提取电子的3维运动速度计算横纵速度比。在阳极电压和阴极电流变化的条件下,对电子速度比和速度零散随之而变化的情况进行了模拟,得到平均速度比1.1和平均速度零散9.5%的结果。基于电子平均半径,并根据电子平均半径与横向速度、纵向速度的关系提出了一种实验测量速度比的方法。当电子轰击荧光屏玻璃时,玻璃上的荧光物质感应到光斑,测量空心光斑的平均半径可计算得到电子速度比,其结果与模拟值误差15%。     

二次谐波回旋行波管Cusp电子枪的模拟与实验研究

 利用3D PIC软件和乌克兰开发的电子光学计算软件TAU对二次谐波回旋行波管Cusp电子枪进行模拟,提取电子的3维运动速度计算横纵速度比。在阳极电压和阴极电流变化的条件下,对电子速度比和速度零散随之而变化的情况进行了模拟,得到平均速度比1.1和平均速度零散9.5%的结果。基于电子平均半径,并根据电子平均半径与横向速度、纵向速度的关系提出了一种实验测量速度比的方法。当电子轰击荧光屏玻璃时,玻璃上的荧光物质感应到光斑,测量空心光斑的平均半径可计算得到电子速度比,其结果与模拟值误差15%。     

Quantum Variance of Maass-Hecke Cusp Forms

In this paper we study quantum variance for the modular surface X=G\\mathbbH{X=\Gamma\backslash\mathbb{H}}, where G = SL₂(\mathbbZ){\Gamma=SL_2(\mathbb{Z})} is the full modular group. We evaluate asymptotically the quantum variance, which is introduced by S. Zelditch and describes the fluctuations of a quantum observable. It is shown that the quantum variance is equal to the classical variance of the geodesic flow on S*X, the unit cotangent bundle of X, but twisted by the central value of the Maass-Hecke L-functions.     

Resonating group kernels for complex cluster systems

The Bargmann transform technique has been generalized to evaluate the resonating group kernels needed for the microscopic cluster model in which constituent fragments are described by harmonic oscillator functions with unequal width parameters. All the techniques developed for the case of equal width parameters are applicable without any change except for a slight modification of the transformation to the Bargmann space cluster-internal and cluster-relative motion vectors. The inversion of the Bargmann transformation has been carried out for those Bargmann transforms which appear in the cluster model, making it possible to gain the kernels in a closed algebraic form. The kernels for the α + d and 9-quark 3-nucleon systems have been evaluated to illustrate the technique.     

Rydberg transitions for positron-hydrogen collisions

e⁺ + H(ns) ↦e⁺ + H(n^′s) transitions for arbitrary n and n^′ have been studied using the distorted-wave formalism in the momentum space [Ghoshal and Mandal, Phys. Rev. A 72, 032714 (2005)]. The distorted-wave scattering amplitudes have been written in a simple closed analytical form. A detailed study has been made on differential and total cross sections in the energy range 20–300 eV. Resonance-like behaviour of the differential cross section has been observed in the the region of lower scattering angles for high Rydberg transitions. To the best of our knowledge the distorted-wave results for differential and total cross sections for such arbitrary transitions are reported for the first time in the literature.     

Cusp of Non-Gaussian Density of Particles for a Diffusing Diffusivity Model

We study a two state “jumping diffusivity” model for a Brownian process alternating between two different diffusion constants, D+>D−, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times, Gaussian behavior with an effective diffusion coefficient is recovered. We show that, for equilibrium initial conditions and when the limit of the diffusion coefficient D−⟶0 is taken, the short time behavior leads to a cusp, namely a non-analytical behavior, in the distribution of the displacements P(x,t) for x⟶0. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state D+ to a δ-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non-analyticity in P(x,t). We demonstrate how super-statistical framework is a zeroth order short time expansion of P(x,t), in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.     

Cusp values and electron densities at coalescence

The correlation between errors in (a) calculated cusp values and (b) calculated electron densities at coalescence are examined for the electron-nucleus and electron-electron pairs in helium. Calculations for 25 fully optimized variational wavefunctions for the ground state are presented. Although a wide variety of functional forms are represented in the set of wavefunctions studied, a strong correlation between (a) and (b) is obtained in the case of the electron-nucleus pair, and a weaker but still significant correlation is found for the electron-electron pair.     

Cusp Interaction in Minimal Length Quantum Mechanics

The modified Schrödinger equation with a minimal length is considered under a Cusp potential which includes the exponential interaction. Next, exact analytical solutions of the problem are reported and thereby the scattering states as well as the corresponding transmission and reflection coefficients are reported.     

Semi-Dispersing Billiards with an Infinite Cusp I

 Let be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f. Under certain conditions on f, we prove that the billiard flow in Q has a hyperbolic structure and, for some examples, that it is also ergodic. This is done using the cross section corresponding to collisions with the dispersing part of the boundary. The relevant invariant measure for this Poincaré section is infinite, whence the need to surpass the existing results, designed for finite-measure dynamical systems. Received: 1 May 2002 / Accepted: 13 May 2002 Published online: 22 August 2002     

Parton distributions for high energy collisions

Recent data from deep inelastic scattering experiments atx10^–2 are used to fix the parton distributions down tox10^–4 andQ ²0.3 GeV². The predicted extrapolations are uniquely determined by the requirement of avalence-like structure ofall parton distributions at some low resolution scale and are furthermore shown to be insensitive in the small-x region, 10^–4x10^–2, to the detailed experimental input at the presently accessiblex>10^–2. Simple parameterizations of the resulting parton distributions are presented in the range 10^–5x<1 and=">Q ²10⁸ GeV² as obtained from the leading- and higher-order evolution equations.