Optical Glucose Monitoring Based on Femtosecond Two-Color Pulse Interferometry

We demonstrate the potential of femtosecond two-color pulse interferometry for in vitro optical glucose monitoring, by dispersion of the group refractive index in a glucose solution sample with respect to a red-color light and a blue-color light. By comparison with femtosecond one-color pulse interferometry, the basic performance of the present system with regard to sensitivity, quantitativeness, and tolerance to surrounding disturbances, is evaluated. The resulting accuracy and precision of glucose determination are 77 and 118mg/dl for 10-mm-sample-thickness, respectively. This near-common-path configuration of the two-color pulse light provides good stability to fluctuations of sample temperature, which is important in clinical applications. Considering the performance of femtosecond two-color pulse interferometry as an optical glucose sensor, a suitable measurement site for in vivo optical glucose monitoring is discussed.     

大尺度有效引力的E(2)规范理论模型

微波背景辐射的低l极矩的各向异性可能不能用微波背景辐射静止系boost到本动参考系来解释,我们推断boost对称性在宇宙学尺度上缺失,又由于单纯结合广义相对论和物质结构的标准模型不能解释星系以上尺度的引力现象,需要引入暗物质和暗能量.而迄今为止所有寻找暗物质粒子的实验给出的都是否定结果,暗能量的本质更是一个谜.因此,我们假设洛伦兹对称性是从星系以上尺度开始部分破缺,以非常狭义相对论对称群E(2)为例,用E(2)规范理论来构造大尺度有效引力理论,并分析了此规范理论的自洽性.从这些讨论中发现,当物质源即使为普通标量物质时,contortion也一般非零,非零contortion的存在会贡献一个等效能量动量张量的分布,它可能对暗物质效应给出至少部分的贡献.我们从对称性出发修改引力,有别于其他的修改引力理论.     

张量重正化群方法及其应用

张量重正化群方法是近年来发展起来的一种新的数值计算方法,它将经典配分函数和量子波函数的张量网络表示与重正化群方法相结合,在强关联系统的数值研究中,发挥着越来越重要的作用。文章以经典统计模型和量子格点模型为例,简要介绍了张量重正化群的一些基础知识和研究给定物理模型的一般性思路,并对张量重正化群未来可能的发展方向和亟待解决的问题进行了讨论。     

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ_z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω) ∝ω~s is found to be universal and independent of the bias ε and the coupling strength α(except at the quantum critical point α = αc and ε = 0). Our NRG data also show C(ω) ∝χ~2ω~s for a wide range of parameters, including the biased strong coupling regime(ε = 0 and α α_c), supporting the general validity of the Shiba relation. Close to the quantum critical point αc,the dependence of C(ω) on α and ε is understood in terms of the competition between ε and the crossover energy scale ω_0~*of the unbiased case. C(ω) is stable with respect to ε for ε《ε~*. For ε》ε~*, it is suppressed by ε in the low frequency regime. We establish that ε~*∝(ω_0~*)~(1/θ)holds for all sub-Ohmic regime 0≤s 1, with θ = 2/(3s) for 0 s≤1/2 and θ = 2/(1 + s) for 1/2 s 1. The variation of C(ω) with α and ε is summarized into a crossover phase diagram on the α–ε plane.     

Acoustic-electromagnetic slow waves in a periodical defective piezoelectric slab

Coupled slow waves, slow acoustic waves, and electromagnetic waves are simultaneously achieved based on a piezoelectric material, in which a line defect is created within a honeycomb lattice array of cylindrical holes etched in a LiNbO_3 slab. Finite element simulations in frequency domain and time domain demonstrate that a highly localized slow mode is obtained in the defect. Owing to the piezoelectricity of LiNbO_3, acoustic and electromagnetic waves are coupled with each other and transmit along the line defect. Therefore, in addition to a slow acoustic wave, an electromagnetic wave with a group velocity even lower than conventional acoustic waves is achieved.     

Quaternionic complexes

Each regular or semi-regular integral affine orbit of the Weyl group of gl(2n + 2, ) invariantly determines a locally exact differential complex on a 4n dimensional quaternionic manifold. This gives quaternionic analogues of Dolbeault cohomology on complex manifolds. We compute the index of such complexes in the hyper-Kähler case, showing that quaternionic cohomology is not trivial.     

A renormalization group explanation of numerical observations of analyticity domains

A recent paper considers the dependence of the size of analyticity domains of some functions appearing in KAM theory as a function of the distance to breakdown. They tentatively conclude that the relation is linear. In this note we argue that McKay's renormalization group picture predicts a power-law dependence with an exponent close to 1 but not equal to 1.     

Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.     

Deterministic chaos in one-dimensional maps—the period doubling and intermittency routes

This paper is a review of the present status of studies relating to occurrence of deterministic chaos and its characterization in one-dimensional maps. As our primary aim is to introduce the nonspecialists into this fascinating world of chaos we start from very elementary concepts and give sufficient arguments for clarity of ideas. The two main scenarios during onset of chaos viz. the period doubling and intermittency are dealt with in detail. Although the logistic map is often discussed by way of illustration, a few more interesting maps are mentioned towards the end.     

利用群速度匹配的级联二阶非线性实现超短激光脉冲压缩

提出了一种采用倾斜脉冲的级联二阶非线性来实现超短激光脉冲压缩的方法. 对基于单块BBO晶体中基频光与倍频光群速度匹配的级联二阶非线性的脉冲压缩方案进行了理论分析. 对比研究了群速度匹配与失配情况下利用级联二阶非线性进行脉冲压缩的效果, 并模拟分析了基频光与倍频光的位相失配量、非线性晶体长度、 基频光初始峰值光强和初始脉宽等因素对脉冲压缩效果的影响. 结果表明, 基频光与倍频光的群速度匹配将会大幅度改善压缩脉冲的时间波形和频谱分布. 通过对位相失配量、晶体长度、初始光强等参数的优化和选取可获得较理想的压缩效果. 采用倾斜脉冲的级联二阶非线性的脉宽压缩方法, 针对中心波长800 nm、脉宽100 fs, 峰值光强为50 GW/cm²的基频光脉冲, 采用25 mm厚BBO晶体, 当基频光与倍频光位相失配量Δk=60 mm^-1(对应失谐角1.98°), 晶体外部脉冲前沿倾斜角γ₀=74°时, 计算获得了质量较好的20 fs剩余基频光, 并同时产生了14 fs的倍频光. 关键词： 倾斜波 级联二阶非线性 群速度失配 脉冲压缩