简并谱的涨落统计特征分析

通过引入权重的方式,使简并谱的积累函数形式上连续递增,并用带权重的多元线性拟合提取涨落谱,由此建立了一套适用于分析简并谱的ＮＮＳ分布、谱刚度、能谱分维函数等涨落统计特征的方法,并具体分析了Ｈ２Ｏ、ＮＨ３及ＣＨ４分子的振动能谱进行涨统计特征分析：发现它们的规则谱和约化非简并谱的涨落统计特征均已非Ｐｏｉｓｓｏｎ化;而且约化非简并谱的非Ｐｏｉｓｓｏｎ化程度较规则谱明显,即前者的能级斥力较后者大;此外,随     

能谱涨落统计特征稳定性分析

通过引入权重,并用一能级数等于简并谱的无趋向性序列为标准去衡量 简并邻间距谱的趋向性,由此建立分析简并谱涨落统计特征稳定性的MKS无参量试验法;根 据该方法,具体分析、比较了H2O分子低激发态与高激发态振动能谱涨落统计特征,找出 了从低激发态向高激发态过度时涨落统计特征明显改变点。     

Rydberg原子研究的新方法

本文首次用非简并四波混频测量了钠原子的Rydberg态系列光谱,并就其某一条谱线在不同压力下的碰撞加宽进行研究.     

纠缠相干态光场驱动下∧-型三能级原子的辐射谱

采用时间演化算符方法,研究∧-型=三能级原子与纠缠相干态光场共振相互作用的辐射谱.给出了辐射谱一般公式,并讨论在纠缠相干态光场驱动下的辐射频谱结构.结果表明,无论下能级简并与否纠缠相干态光场平均光子数很小时均出现拉比分裂,且强度随双模光场纠缠程度的增加而增加.当两下能级简并时,若两模场的平均光子数较小,辐射谱呈现对称多峰结构,若两模场的平均光子数较大,辐射谱呈现对称五峰结构.当两下能级非简并时,若两模场的平均光子数较小,辐射谱呈现对称多峰结构.若两模场的平均光子数较大,辐射谱呈现对称十峰结构.纠缠相干光与非纠缠相干光辐射谱的本质差别有两点:一是双模光场强量子关联导致纠缠度越强拉比峰强度越高;二是存在纠缠时由于两模场相干性导致辐射谱呈现对称多峰结构.     

多普勒系统中简并四波混频的饱和效应

我们研究了多普勒增宽的二能级系统中,简并四波混频的饱和效应。推导出一组适合数字分析的递推公式。利用此公式,计算了近饱和区,简并四波混频信号的线形。计算结果表明,随着光强的增加,谱线中心将分裂成双峰。 关键词：     

掺金单晶硅特性的研究

本文研究单晶硅掺金前后的表面光伏和红外吸收谱,证实在相同表面状况下,红外吸收谱的基线与少子扩散长度的对应关系;由半导体统计,推导出简并因子不等于1时扩金硅的统计公式,以及金受主简并因子g_Au,a≠1,金施主简并因子g_Au,d≠1硅双重能级复合理论公式,由此计算的少子寿命值与测量值之比在1.64—0.745之间。 关键词：     

基于简并二能级原子系统的电磁诱导增益

理论和实验研究了基于简并二能级原子系统的电磁诱导增益(EIG)效应,构建了一个N型简并二能级系统,分析了在不同多普勒频移下信号光增益随抽运光拉比频率的变化规律。结果表明:在增大区间,增益谱一直保持线宽极窄的单峰结构;而在减小区间,增益谱产生类拉比分裂,并且呈现出对称的双峰结构。选择Cs原子基态和激发态角动量相同条件下的简并能级结构,实验研究了EIG的产生特点,并进一步分析了抽运光强度及信号光偏振对增益峰值效率的影响。     

压缩真空库场中二能级原子的非简并双光子荧光谱

利用投影算符技巧从刘维方程出发导出了二能级原子约化密度算符主方程，研究了压缩真空库场中二能级原子的非简并双光子荧光谱特性.发现与真空库或热库中双光子荧光不同，在非简并双光子情况中存在一种新型振荡现象，它具有上下两个阈值，在上下阈值之间原子发生振荡，在两阈值之外原子将不发生振荡.在两阈值之间原子的非简并双光子荧光谱呈现正峰结构，在两阈值之外双光子荧光谱具有负的峰结构.光谱形状强烈地依赖于双光子自然线宽，但光谱是非相敏性的，这是未曾预料到的. 关键词：     

双负介质对光子晶体透射能带谱的简并效应研究

利用传输矩阵法理论,通过数值计算模拟的方法,研究双负介质对一维光子晶体透射能带谱的影响。结果表明:当C介质由双正介质变成双负介质时,光子晶体(CBAABC)n的禁带、能带和光子晶体(AB)m(CBAABC)n(BA)m的透射峰均出现明显的简并现象,即前者相邻多禁带和多能带结构简并为较宽的单禁带和单能带结构,后者的透射峰由2n+1条简并成2n-1条;当双负介质C的光学厚度负值减小时,光子晶体(AB)m(CBAABC)n(BA)m的透射峰向禁带中心靠拢,出现简并趋势。双负介质对光子晶体透射能带谱的简并效应,为光子晶体设计光学滤波器件、光学开关等提供参考。     

应用双非简并四波混频理论研究原子的碰撞效应

在己有实验的基础上,提出了由双光子共振非简并四波混频和碰撞再构非简并四波混频组成用于研究原子碰撞效应的双非简并四波混频理论,分析了缓冲气压、温度、共振失谐和碰撞展宽系数对双非简并四波混频谱线的影响.在由基态、中间态和激发态组成的级联三能级系统中,双非简并四波混频可同时研究碰撞引起的激发态谱线展宽和碰撞引起的中间态能级再分布现象.与测量纵向弛豫碰撞展宽的传统实验方法不同,本文方法是一种纯光学的相干测量技术,可以同时测量激发态与基态间的横向弛豫Γ_(20)和中间态与基态间的横向弛豫Γ_(21)的碰撞展宽.     

The nature of the spectrum for a Landau Hamiltonian with delta impurities

We consider a single-band approximation to the random Schrödinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the entire spectrum of this Hamiltonian when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level in the absence of a random potential being infinitely degenerate, while the eigenfunctions corresponding to energies in the rest of the spectrum are localized.     

Characterization of the Spectrum of the Landau Hamiltonian with Delta Impurities

We consider a random Schr?dinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the spectrum in the lowest N Landau bands of this random Hamiltonian when the magnetic field is sufficiently strong, depending on N. We show that the spectrum in these bands is entirely pure point, that the energies coinciding with the Landau levels are infinitely degenerate and that the eigenfunctions corresponding to energies in the remainder of the spectrum are localized with a uniformly bounded localization length. By relating the Hamiltonian to a lattice operator we are able to use the Aizenman–Molchanov method to prove localization. Received: 1 June 1998 / Accepted: 29 January 1999     

定向凝固过程中枝晶侧向分枝生长行为与强制调控规律

采用相场法数值模拟研究了定向凝固过程中随机噪声条件下枝晶侧向分枝生成行为与强制扰动条件下侧向分枝调控规律. 模拟结果表明: 随机噪声条件下, 侧向分枝整体上并无规则性, 但产生频率存在一定分布范围, 且在一定时间段内会出现生成频率一致且具有极强相关性的一组侧向分枝, 即波包; 不同波包之间不具有相关性, 但不同波包内部的侧枝生成频率基本相同, 且与侧枝整体频谱曲线峰值位置处的频率基本相当; 强制周期扰动条件下, 当扰动频率处于侧向分枝整体生成频率范围内时, 可激发枝晶产生规则侧向分枝, 且扰动频率与波包内侧枝生成频率一致时侧向分枝最发达. 研究结果可为向定向凝固枝晶形态的调控提供理论指导.     

The Canopy Graph and Level Statistics for Random Operators on Trees

For operators with homogeneous disorder, it is generally expected that there is a relation between the spectral characteristics of a random operator in the infinite setup and the distribution of the energy gaps in its finite volume versions, in corresponding energy ranges. Whereas pure point spectrum of the infinite operator goes along with Poisson level statistics, it is expected that purely absolutely continuous spectrum would be associated with gap distributions resembling the corresponding random matrix ensemble. We prove that on regular rooted trees, which exhibit both spectral types, the eigenstate point process has always Poissonian limit. However, we also find that this does not contradict the picture described above if that is carefully interpreted, as the relevant limit of finite trees is not the infinite homogenous tree graph but rather a single-ended ‘canopy graph.’ For this tree graph, the random Schrödinger operator is proven here to have only pure-point spectrum at any strength of the disorder. For more general single-ended trees it is shown that the spectrum is always singular – pure point possibly with singular continuous component which is proven to occur in some cases.     

Bispectrum Analysis of One-Dimensional Regular Fractals with Additive Random Noise

The bispectrum of the Cantor set that is a typical regular fractal is calculated and its fractalities are shown. A relation between the bispectrum and the fractal dimension of the object is elucidated. Effects of additive random noise on the scaling property of the bispectrum are compared with those of the corresponding power spectrum.     

Diffusion of charged particles in strong large-scale random and regular magnetic fields

The nonlinear collision integral for the Green’s function averaged over a random magnetic field is transformed using an iteration procedure taking account of the strong random scattering of particles on the correlation length of the random magnetic field. Under this transformation the regular magnetic field is assumed to be uniform at distances of the order of the correlation length. The single-particle Green’s functions of the scattered particles in the presence of a regular magnetic field are investigated. The transport coefficients are calculated taking account of the broadening of the cyclotron and Cherenkov resonances as a result of strong random scattering. The mean-free path lengths parallel and perpendicular to the regular magnetic field are found for a power-law spectrum of the random field. The analytical results obtained are compared with the experimental data on the transport ranges of solar and galactic cosmic rays in the interplanetary magnetic field. As a result, the conditions for the propagation of cosmic rays in the interplanetary space and a more accurate idea of the structure of the interplanetary magnetic field are determined.     

Use of random numbers in computer simulation of magnetic resonance signals

The proton magnetic resonance spectra of water molecules diffusing over regular sites in natrolite are numerically simulated. Experimental data and the results of simulation are found to be in good agreement in a wide temperature interval including the transition range, where the magnetic resonance spectrum is a superposition of a wide unaveraged spectrum and a spectrum averaged by the motion of molecules. The simulation uses generators of pseudorandom-number Markovian sequences. For a binary Markovian process, it is shown, in particular, that the time within which a physical quantity remains constant is described by an exponentially distributed random number.     

Interaction of regular and chaotic states

Modelling the chaotic states in terms of the Gaussian Orthogonal Ensemble of random matrices (GOE), we investigate the interaction of the GOE with regular bound states. The eigenvalues of the latter may or may not be embedded in the GOE spectrum. We derive a generalized form of the Pastur equation for the average Green’s function. We use that equation to study the average and the variance of the shift of the regular states, their spreading width, and the deformation of the GOE spectrum non-perturbatively. We compare our results with various perturbative approaches.     

Frequency/time domain modeling of a direct drive point absorber wave energy converter

Two different methods to model a point absorber wave energy converter(WEC)with direct drive linear power take-off(PTO)are proposed in the present study:the frequency domain(FD)method and the time domain(TD)method.In the FD analysis,the frequency response function(FRF)of the WEC device is obtained via the equation of motion,and the expressions of power capture width in regular and random waves are derived as well.In the TD modeling,based on a state space approximation of the convolution term in the motion equation,both regular wave and random wave simulations are carried out.The regular wave simulation results indicate that the state space approximation is sufficiently accurate and the capture width reaches the maximum in the vicinity of the natural frequency.In the random wave simulations,the effects of buoy size,the PTO damping and wave climate on the power capture width are discussed in detail,which leads to the conclusion that the capture widths are influenced by the natural frequency of the WEC device,peak frequency of the wave spectrum,the amplitude of FRF and PTO damping.Furthermore,the increase of the capture width is at the cost of a relatively large buoy size and PTO damping when control is not included.     

Spectral fluctuations and 1/f noise in the order-chaos transition regime

Level fluctuations in a quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate the level fluctuations to the classical dynamics in the regular and chaotic limit. In this, we show that the spectrum of the system undergoing order to chaos transition displays a characteristic f(-gamma) noise and gamma is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles, respectively, of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.