2+1维SU(2)格点胶球质量的变分计算

本文对具有严格基态解和正确经典连续极限的格点规范哈密顿量,采用变分法,计算了2+1维SU(2)规范群的胶球质量,得到在1.3≤1/g²≤7范围内,标度行为是am=2.28g²,这与弱耦合展开及另一没有正确连续极限的哈密顿量的结果一致.     

非长波极限下二维光子晶体中横电模的等效介质理论

基于Mie散射理论, 推导、建立了适用于非长波极限的二维光子晶体中横电模的等效介质理论. 随后利用该理论探讨了二维光子晶体中横电模的负折射特性和零折射特性, 计算结果与相应的能带结构相符合, 验证了该理论在非长波极限条件下的适用性. 更进一步的是, 使用该理论能得到从能带结构中无法获取的额外信息.     

FBG应变传感器应力疲劳极限传感寿命评估方法

光纤光栅应变传感器在应力疲劳作用下不可避免地出现性能衰退,为了评估其极限传感寿命,从光纤光栅传感原理出发,理论推导了应力疲劳作用引起的满度相对误差表达式,以工业仪表精确度等级作为传感器的极限状态阈值,提出了基于等强度梁的极限传感寿命测试方法.利用该方法评估了高桩码头结构健康监测应用环境中光纤光栅应变传感器的极限传感寿命,以满度相对误差变化4%作为极限失效阈值,对4支传感器进行了1.32亿应力疲劳实验.当疲劳至1.32亿次时,2支传感器达到极限传感寿命,1支传感器接近极限传感寿命,即极限传感寿命约为1.32亿次.实验结果表明,提出的方法能有效地测试不同结构健康监测需求下,光纤光栅应变传感器的应力疲劳极限传感寿命.     

动态质量密度和声学超常介质

复合介质的质量密度通常认为是组成它的各种成分的质量密度的体平均值.体平均质量密度常常被用于计算在长波长极限下的声波速度,在此极限下波长比复合介质中的特征尺度要大得多.作者通过严格的数学推导证明,计算(长波长极限下的)波速时所用到的动态质量密度与静态的体平均质量密度有显著的不同.这一发现与最近的实验结果符合得非常好,并且使得声学超常介质的实现成为可能.这两种质量密度之所以不同的物理根源就在于,在波场中复合介质中的各个成分之间有相对的运动.也就是说,隐含的假定——在长波长极限下复合介质中的各个成分必定会全体同相地运动——将不再正确,尤其是当各个成分的声学阻抗之间有较大的差异时.实验和理论显示,对于局域共振声学材料而言,动态质量密度甚至还会变成是负的.文章探讨了这一发现的物理意义,以及它在声学超常介质领域的应用.     

理论研究强激光场中2pz态氢原子的电离

运用强场近似速度规范理论研究了激发态氢原子的电离情况,当ω1a.u.,γ1时(ω是激光场的频率,γ是Keldysh绝热参数),在线性极化激光场中推导了2pz态氢原子电离率的简单表达式,从公式中可以看出在低频极限的情况下,电离率和激光场频率ω成正比,这一公式对激发态氢原子电离机制的研究提供了重要的理论参考.     

理论研究强激光场中2pz态氢原子的电离

运用强场近似速度规范理论研究了激发态氢原子的电离情况,当 a.u. 时（ω是激光场的频率,γ是Keldysh绝热参数）,在线性极化激光场中推导了2pz态氢原子电离率的简单表达式,从公式中可以看出在低频极限的情况下,电离率和激光场频率ω成正比,这一公式对激发态氢原子电离机制的研究提供了重要的理论参考。     

Li_2部分电子态的完全振动能谱与离解能的精确研究

本文将孙卫国等建立的精确计算双原子分子离解能的解析表达式作为分子振动能级正确收敛的重要物理判据,应用代数方法,进一步研究了重要的碱金属Li2的5个电子态的完全振动能谱和离解能,获得了这些电子态的精确振动光谱常数,同时也得到了包括接近分子离解极限在内的完全振动能谱和与实验值符合得很好的理论离解能.这些计算结果为许多需要这些电子态振动数据的研究领域提供了重要的研究数据.     

诱导引力理论中的Baby宇宙

本文讨论诱导引力理论中Baby宇宙的量子效应.我们证明了在诱导引力理论中Baby-Parent宇宙相互作用是非定域的,并论证了在低能极限下诱导的宇宙学常数为零.这一论证并不依赖于诱导势的细节.     

近距离激光外差探测光学极限位移分辨率

通过统计理论和维纳-辛钦定理推导出激光外差探测系统光电流的功率谱函数,分析了光电流谱线分布与激光光源线宽、中频信号频率以及信号光相对本振光传输延迟时间的关系,修正了相关文献中光电流功率谱的理论公式.根据信号与噪声理论建立了激光线宽引起的相位噪声的一维概率分布模型,并据此得到了基于激光波长、探测距离以及激光线宽的极限位移分辨率的数学模型.对光电流的功率谱和外差光学极限位移分辨率进行了相关的数值仿真,结果表明延迟时间与相干时间的关系决定光电流谱线分布的情况.当激光波长为532 nm,激光线宽在1 kHz,探测距离为100 m时,光学极限位移分辨率为0.266 nm,相关文献中的实验数据与理论推导结果相符合.     

费米超流气体的非线性Rosen-Zener隧穿

以非线性Rosen-Zener隧穿理论为基础, 用平均场近似的方法, 通过考虑高阶非线性项的影响, 研究了非线性两能级系统中费米超流气体的Rosen-Zener隧穿现象. 研究发现粒子间的非线性相互作用能够显著地影响量子隧穿. 分别在快扫描极限和绝热极限的条件下, 解释了Rosen-Zener隧穿现象, 并给出了矩形振荡周期与非线性参数之间的依赖关系. 这为更深入认识费米气体的基本属性提供了理论基础.     

Long-time limit behavior of the solution to an atom＇s master equation

We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.     

Hopf Bifurcation Control of a Hyperchaotic Circuit System

This paper is concerned with the Hopf bifurcation control of a new hyperchaotic circuit system. The stability of the hyperchaotie circuit system depends on a selected control parameter is studied, and the critical value of the system parameter at which Hopf bifurcation occurs is investigated. Theoretical analysis give the stability of the Hopf bifurcation. In particular, washout filter aided feedback controllers are designed for delaying the bifurcation point and ensuring the stability of the bifurcated limit cycles. An important feature of the control laws is that they do not result in any change in the set of equilibria. Computer simulation results are presented to confirm the analytical predictions.     

Deformation of Towers of Algebras and Quantized Intersection Cardinality Functions

The inductive limit of a tower of separable algebras is unchanged, up to isomorphism, by consistent deformations but the inductive limit of a corresponding tower of modules may be nontrivially deformed, thereby quantizing the limit module. In the case of the inductive limit of the complex group algebras of the symmetric groups and their deformations, the Hecke algebras, this quantization preserves properties of the finite case which disappear in the absence of quantization.     

Limit of Quasilocal Mass at Spatial Infinity

We study the limit of quasilocal mass defined in [4 and 5] for a family of spacelike 2-surfaces in spacetime. In particular, we show the limit coincides with the ADM mass at spatial infinity. The limit for coordinate spheres of a boosted slice of the Schwarzchild solution is computed explicitly and shown to give the expected energy-momentum four-vector.     

Multi-scale Analysis of Compressible Viscous and Rotating Fluids

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter . If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account.     

Deformed dispersion relation constraint with hydrogen atom 1S-2S transition

We use the latest results of the ultra-high accuracy 1S-2S transition experiments in the hydrogen atom to constrain the forms of the deformed dispersion relation in the non-relativistic limit.For the leading correction of the non-relativistic limit,the experiment sets a limit at an order of magnitude for the desired Planck-scale level,thereby providing another example of the Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory experiments.For the next-to-leading term,the bound is two orders of magnitude away from the Planck scale,however it still amounts to the best limit,in contrast to the previously obtained bound in the non-relativistic limit from the cold-atom-recoil experiments.     

Theoretical study of the accuracy limits of optical resonance frequency measurements

The principal limits for the accuracy of the resonance frequency measurements set by the asymmetry of the natural resonance line shape are studied and applied to the recent accurate frequency measurements in the two-photon 1s-2s resonance and in the one-photon 1s-2p resonance in a hydrogen atom. This limit for 1s-2s resonance is found to be approximately 10(-5) Hz compared to the accuracy achieved in experiment +/-46 Hz. In the case of a deuterium atom the limit is essentially larger: 10(-2) Hz. For 1s-2p resonance the accuracy limit is 0.17 MHz while the uncertainty of the recent frequency measurement is about 6 MHz.     

Why is super-resolution so inefficient?

Many optical imaging systems have been designed to achieve spatial resolution exceeding the limit proposed by Abbe theory, namely lambda/2NA. These systems invariably use light inefficiently. We discuss the application of information theory to this problem, in an effort to find an upper limit to the theoretical efficiency of a super-resolving system, as a function of the degree to which its capabilities exceed the Abbe limit.     

On the fatigue properties of high-strength steels

Summary The paper gives the results of an investigation of the optimal tensile strength level suitable for obtaining the maximum fatigue limit of a Mn-Cr-Ni-Mo steel produced by current technology with constant amount of alloying elements, but three different carbon contents, 0·21–0·41%, after conventional (CT) and thermomechanical treatment (TMT). The study was carried out in an effort to explain the considerable difference in the fatigue limit data of high strength steels published by different authors [1, 2, 3]. For a tensile strength of about 260 kp/mm² the fatigue limits were found from 38 up to 116 kp/mm².In addition to confirming the influence of the TMT on the tensile strength and ductility already known, it was found that the maximum of the fatigue properties for medium carbon content can be obtained in the tensile strength area of cca 220 kp/mm². When the tensile strength is raised beyond this limit the fatigue limit falls. The values of the fatigue limit after CT as well as after TMT, but in comparison to the same tensile strength range, are very similar. The fatigue limits of about 90 kp/mm² lie within the great range of other published data.Suggested causes for the decreased fatigue limit at high strength such as the method of testing, the shape of the test bar, the effect of ductility, the grain size and the level of internal stresses, are discussed and the idea is advanced that the main cause of the great differences is the increasing influence of the size of non-metallic inclusions as the strength increases.As a result, a preliminary hypothesis was made to explain the relation of the fatigue limit of steels to the size of non-metallic inclusions, referred to different limits of strength, based on the results of Stulen and co-workers [4]. By means of extrapolation the fatigue limit of a steel containing an inclusion of 0 m diameter was also determined as a function of the tensile strength. This can be considered as the theoretical fatigue limit of the metal matrix itself, where the mechanism of the fatigue fracture is controlled by the fatigue phenomena in the matrix itself. Below this limit, on the contrary, the mechanism of the fatigue fracture is controlled by the presence of nonmetallic inclusions.     

High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables

We experimentally demonstrate continuous-variable quantum teleportation beyond the no-cloning limit. We teleport a coherent state and achieve the fidelity of 0.70 +/- 0.02 that surpasses the no-cloning limit of 2/3. Surpassing the limit is necessary to transfer the nonclassicality of an input quantum state. By using our high-fidelity teleporter, we demonstrate entanglement swapping, namely, teleportation of quantum entanglement, as an example of transfer of nonclassicality.