Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length

The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature （Phys. Rev. Lett. 94（2005）050402 and Chin. Phys. Lett. 22（2005） 1855）.

Alternative scattering kernels for the first estimates of a reactor:diffusion length

Diffusion-length calculations of neutrons are performed using the Chebyshev polynomials of the second kind. The neutrons are assumed to move with constant energy in a uniform homogeneous slab. An alternative scattering kernel called an Anl?–Gngr phase function and a traditional Henyey–Greenstein phase function are used for the scattering function in the stationary neutron transport equation. First, analytic expressions and then numerical results are obtained for the diffusion length for various values of the scattering and cross-sectional parameters.Numerical results obtained from both scattering kernels for the diffusion length of the neutrons are given in tables side by side for comparison. The applicability of the method is easily demonstrated by these results.

Effect of Time-Dependent Atomic Scattering Length on Solitons in Bose-Einstein Condensates with a Complex Potential

We consider the one-dimensional nonlinear Schrǒdinger equations that describe the dynamics of a Bose-Einstein Condensates with time-dependent scattering length in a complex potential. Our results show that as long as the integrable relation is satisfied, exact solutions of the one-dimensional nonlinear Schrǒdinger equation can be found in a general closed form, and interactions between two solitons are modulated in a complex potential We find that the changes of the scattering length and trapping potential can be effectively used to control the interaction between two bright soliton.

Analyzing Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length

We analyze the dynamics of a bright soliton in atomic scattering length in an expulsive parabolic potential. Bose-Einstein condensates （BECs） with time-dependent Under a safe ravage of parameters in which the Gross-Pitaevskii （GP） equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomic scattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.

Solitons in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in a Harmonic Trap

We obtain the integrable relation for the one-dimensional nonlinear Schrodinger equations which describes the dynamics of a Bos-Einstein Condensates with time-dependent scattering length in a harmonic potential. The exact one- and two-soliton solutions are constructed analytically by using the Hirota method. Then we further discuss the dynamics of the one soliton and the interactions between two solitons in currently experimental conditions.

Lattice QCD Calculation of ππ Scattering Length

We study s-wave pion-pion scattering length in lattice QCD for pion masses ranging from 330 MeV to 466 MeV. In the ＂Asqtad＂ improved staggered fermion formulation, we measure full ππ four-point correlators for isospin I = 0 and 2 channels, and use chiral perturbation theory at next-to-leading order to extrapolate our simulation results. Extrapolating to the physical pion mass yields scattering lengths as mna01=2 = -0.041 6（2） and mna01= 0.186（2） for isospin I = 2 and 0 channels, respectively. Our lattice simulation for ππ scattering length in I = 0 channel is an exploratory study, where we include the disconnected contribution, and our preliminary result is near to its experimental value. These simulations are carried out with MILC 2 ＋ 1 flavor gauge configurations at lattice spacing a ≈0.15 fm.

Dynamics of Periodic Waves in Bose-Einstein Condensate with Time-Dependent Atomic Scattering Length

Evolution of periodic waves and solitary waves in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the mapping deformation method, we successfully obtain periodic wave solutions and solitary wave solutions, including the bright and dark soliton solutions.The results in this paper include some in the literatures [Phys. Rev. Lett. 94 （2005） 050402 and Chin. Phys. Left. 22 （2005） 1855].

The scattering lengths for alkali-metal atoms

The collision of alkali-metal atoms at ultralow temperatures have been studied, The Scattering lengths and the effective range are calculated for 7Li, 23Na, 39K, 87Rb, and 133Cs.

Elastic scattering of sodium and cesium atoms at ultracold temperatures

The elastic scattering properties in a mixture of sodium and cesium atoms are investigated at cold and ultracold temperatures. Based on the accurate interatomic potential for the NaCs mixture, the interspecies s-wave scattering lengths, the effective ranges and the p-wave scattering lengths are calculated by the quantal method and the semiclassical method, respectively. The s-wave scattering lengths are 512.7a0 for the singlet state and 33.4a0 for the triplet state. In addition, the spin-change and elastic cross sections are also calculated, and the g-wave shape resonance is found in the total elastic cross sections.

Accurate calculation of the elastic scattering properties of ^7Li atoms at ultralow temperatures

The elastic scattering properties for collisions between two ^7Li atoms are investigated in the cold and ultracold regimes separately. Based on recent theoretical and experimental results, we present the improved hybrid potentials for the singlet X^1 ∑g^＋ and triplet a^3 ∑u^＋ ground states of the Li2, Our calculated values for the scattering lengths α and the effective ranges re are compared with previous ones, and found them to be in good agreement. The scattering lengths are 34.6α0 for the singlet state and -27.6α0 for the triplet state. Shape resonances occur in the collisions at low energies. We also calculate the total cross sections and the energy positions of shape resonances for both X^1 ∑g^＋ and a^3 ∑u^＋ states.

Calculation of the elastic scattering properties for cold and ultracold 39K atoms in a triplet state

The elastic scattering properties for collisions between cold and ultracold 39K atoms in a triplet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for a triplet α3∑u^＋ ground state of K2. Our calculated value of the s-wave scattering length a by using the Numerov method for the triplet state is 79.578α0 and found to be in good agreement with the previous ones. The numbers of bound states are supported by the molecular potential. Pronounced shape resonances appear for the l = 3 partial waves for the α3∑u^＋ state. Furthermore, the s-wave scattering cross section, the total cross section and energy positions of shape resonances for the α3∑u^＋ state are calculated.

Scattering properties of the ultracold ^(133)Cs_2 triplet state

The elastic scattering properties of ultracold ^133Cs2 triplet state are investigated in detail. We construct a potential curve of the ^133Cs2 triplet state, based on the latest ab initio molecular potential data and show how the scattering parameters are obtained by using three methods： the Numerov method, the semiclassical method and the variable phase method, where the scattering lengths of the ^133Cs2 triplet state, i.e. 301.79a0, 300.67a0 and 310.81a0 are obtained respectively, with a0 being the Bohr radius. We also calculate the effective range and the number of bound states for the ^133Cs2 triplet state. Our results are in agreement with the recent experimental data and the theoretical calculations. This confirms that the results of the scattering properties of the ultracold ^133Cs2 triplet state, calculated by using these three methods, are reliable.

Calculation of scattering parameters for ultracold ~6 Li-~7 Li elastic collisions

This paper theoretically studies the elastic scattering properties in a mixture of 6Li and 7Li atoms at cold and ultracold temperatures. Based on the constructed accurate interatomic potential of the triplet state for 6Li7Li mixture by the mass scaling method, it calculates the interspecies s-wave scattering lengths and the p-wave scattering lengths by the variable phase method and the semiclassical method, respectively. The scattering length is in good agreement with the experiment. The partial-wave and total cross sections are also calculated and a rich resonance structure is found.

Elastic Scattering of Ultracold ^133Cs and SSRb Atoms in Triplet State

Elastic scattering properties of the ultracold interaction for the triplet state of ^133Cs and ^85Rb atoms are studied using two kinds of potentials by the same phase Ф. One is the interpolation potential, and another is Lennard-Jones potential （LJl2,6 ）. The radial Schrodtinger equation is also solved using two computational methods, the semiclassical method （WKB）, and the Numerov method. Our results are found to be in an excellent agreement with the more recent theoretical values. It shows that the two potentials and methods are applicable for studying ultracold collisions between the mixing alkali atoms.

Meson-Meson Scattering on Anisotropic Lattices

Using the tadpole improved Wilson quark action on small, coarse, and anisotropic lattices, meson-meson scattering lengths are calculated within quenched approximation. The study covers pion-pion scattering in the I = 2 channel and kaon-pion scattering in the I = 3/2 channel. The results are extrapolated towards the chiral limit. Finite volume and finite lattice spacing errors are also analyzed and results in the infinite volume and continuum limit are obtained. Our results are compared with the results obtained using Roy equations, chiral perturbation theory, dispersion relations, and the experimental data. We also compare our results with other lattice results on the scattering lengths.

Revisiting the Electron Radius in Light of Length Contraction

In previous work, the electron radius was identified as the “actual electron radius.” However, this is more accurately described as the electron radius at rest. This study reexamines the electron with an emphasis on the electron radius under motion, incorporating the effects of length contraction. The findings suggest that the radius is subject to Lorentz contraction, which has interesting implications for relativistic effects at the subatomic level.

Temperature and volume dependence of pion-pion scattering lengths

The s-wave pion-pion scattering lengths a0 and a2 are studied at finite temperature and in finite spatial volume under the framework of the Nambu-Jona-Lasinio model.The behavior beyond the pseudo transition temperature is investigated using proper time regularization.The scattering length a0 exhibits singularity near the Mott temperature,and a2 is a continuous but non-monotonic function of temperature.We present the effect of finite volume on the scattering length and find that a0 can be negative and its singularity disappears at small volumes,which may hint at the existence of a chiral phase transition with decreasing volume.

理想D空间和理想scattered空间在信息系统中的应用

通过引入理想D空间概念,研究了理想D空间的空间性质,讨论了理想D空间与理想scattered空间的关系,并通过二者在信息系统中的应用实例进行说明。

基于GBK标量散射模型的超光滑光学元件表面特性参数预测方法

在引力波探测系统中,要实现对引力波的高精度测量,超光滑光学元件散射特性至关重要。然而,现有光学元件表面特性参数测量方法难以满足超光滑光学元件的测量需求。针对这一难题,提出了一种基于GBK(Generalized Beckmann-Kirchhoff)标量散射模型的光学元件表面特性参数预测方法。利用GBK标量散射模型和基于光腔衰荡技术的表面散射测量方法,建立了表征超光滑光学元件表面特性参数(表面粗糙度和自相关长度)的方程组,进而利用图解法求解得到超光滑光学元件的表面特性参数。为了验证预测方法的适应性,对不同表面特性参数下的多种待测光学元件进行了预测,获得了不同表面特性参数下元件表面粗糙度和自相关长度预测值的相对误差曲线。结果表明:表面粗糙度在0.1064~1.064 nm范围内时,其预测值相对误差均在1%以内;自相关长度在1064~3192 nm范围内时,其预测值相对误差均在1%以内。因此,在文中提出的表面特性参数范围内,该预测方法能快速准确预测超光滑光学元件的表面特性参数,具有较好的适应性和有效性,可为引力波探测系统中超光滑光学元件散射特性的测量提供参考。

Enhanced spin diffusion length by suppressing spin-flip scattering in lateral spin valves

The spin transport was investigated in permally （Py）/MgO/Ag junction with lateral spin valve structure. Non-local lateral spin valves measurement was carried out to determin, the apin accumulignal in Ag strip, and the spin dif u^sion - length in Ag of the lateral spin valves was extracted from devices with the different distances between injector and detector. The experimental results are found that spin accumulation and spin diffusion length （2s） could be significantly enhanced in Ag strip with MgO capping layer, and those effects may be attributed to the low-surface spin scattering rate in Ag with an MgO cap- ping layer.