The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential

We study the effect of an eigenvalue appearing from the boundary of the essential spectrum of the Schrödinger operator perturbed by a rapidly oscillating compactly supported potential. We prove sufficient conditions for the existence and absence of such an eigenvalue and obtain the first few terms of its asymptotic expansion for the case where this eigenvalue exists.     

Fast-electron optical spectrum of a two-dimensional electron gas in the presence of the Rashba effect

We examine how the Rashba spin-orbit interaction (SOI) affects the fast-electron optical spectrum of a two-dimensional electron gas (2DEG). It is found that for a spin-split 2DEG, the spectrum of optical absorption is mainly induced by plasmon excitation via inter-SO electronic transition. From the width and position of the spectrum, the Rashba spin-splitting can be identified optically and, therefore, important spintronic properties can be measured though optical experiments.     

基于反中值滤波的红外焦平面自适应非均匀性校正方法

分析了红外焦平面阵列非均匀性的噪声特性，提出了一种用反中值滤波为核心的红外焦平面自适应校正的方法。针对实际的图像进行了实验，实验证明该方法在校正效果、收敛速度、对静止目标保持能力及可硬件化等方面都有较好的表现。     

光纤光栅反射谱对非均匀应变的展宽响应

光纤布拉格光栅在非均匀应力场作用下，其纤芯折射率及光栅栅距都将产生非均匀变化，本文给出了光纤光栅与非均匀应变场的相互作用模型，建立了反射谱对非均匀应变的响应关系。并给出了线性应力场的实验结果。     

滤紫外和红外光的荧光玻璃的研制及其应用

研制出了掺铈、钐的滤紫外和红外光的硼硅酸盐荧光玻璃，测试了该玻璃的吸收光谱和荧光谱，并用其做了固体激光器工作物质的紫外和红外滤光套，能使激光效率提高２５％－５０５，从而促进固体激光器的微型化和实用化。     

电子助进化学气相沉积金刚石中发射光谱的蒙特卡罗模拟

采用蒙特卡罗方法，对源料气体为CH4/H2混合气的电子助进化学气相沉积（EACVD）中 的氢原子(H)、碳原子(C)以及CH基团的发射过程进行了模拟.研究了CH4浓度、反应室气压 和衬底偏压等工艺参数对发射光谱及成膜的影响.研究发现，CH基团可能是有利于金刚石薄 膜生长的活性基团，而碳原子不是；偏压的升高可提高电子平均温度及衬底表面附近氢原子 的相对浓度；通过氢原子谱线可测定电子平均温度并找到最佳成膜实验条件.该结果对EACVD 生长金刚石薄膜过程中实时监测电子平均温度，有效控制工艺条件，生长出高质量的金刚石 薄膜具有重要的意义. 关键词： 蒙特卡罗模拟 金刚石薄膜 发射光谱     

Universality in the length spectrum of integrable systems

The length spectrum of periodic orbits in integrable hamiltonian systems can be expressed in terms of the set of winding numbers {M ₁,…,M _f} on thef-tori. Using the Poisson summation formula, one can thus express the density, Σδ(T−T _M), as a sum of a smooth average part and fluctuations about it. Working with homogeneous separable potentials, we explicitly show that the fluctuations are due to quantal energies. Further, their statistical properties are universal and typical of a Poisson process as in the corresponding quantal energy eigenvalues. It is interesting to note however that even though long periodic orbits in chaotic billiards have similar statistical properties, the form of the fluctuations are indeed very different.     

Marked length rigidity for symmetric spaces

We give conditions under which a homomorphism between two Zariski dense subgroups of connected semisimple Lie groups G and G' without compact factors and with trivial center can be extended to a continuous isomorphism between G and G'. In particular we prove the marked length rigidity and the marked translation vector rigidity. This last result was motivated by a Margulis‚s question. Received: September 18, 2001     

Three-dimensional ab initio dipole moment surfaces and stretching vibrational band intensities of the XH3 molecules

Stretching vibrational band intensities of XH₃ (X=N, Sb) molecules are investigated employing three-dimensional dipole moment surfaces combined with the local mode Hamiltonian model.The dipole moment surfaces of NH₃ and SbH₃ are calculated with the density functional theory and at the correlated MP2 level,respectively. The calculated band intensities are in good agreement with the available experimental data. The contribution to the band intensities from the different terms in the polynomial expansion of the dipole moments of four group V hydrides (NH₃, PH₃,AsH₃ and SbH₃) are discussed. It is concluded that the breakdown of the bond dipole approximation must be considered. The intensity “borrowing” effect due to the wave function mixing among the stretching vibrational states is found to be less significant for the molecules that reach the local mode limit.     

Singlet–triplet oscillations and far-infrared spectrum of four-minima quantum-dot molecule

We study ground states and far-infrared spectra (FIR) of two electrons in four-minima quantum-dot molecule in magnetic field by exact diagonalization. Ground states consist of altering singlet and triplet states, whose frequency, as a function of magnetic field, increases with increasing dot–dot separation. When the Zeeman energy is included, only the two first singlet states remain as ground states. In the FIR spectra, we observe discontinuities due to crossing ground states. Non-circular symmetry induces anticrossings, and also an additional mode above ω₊ in the spin-triplet spectrum. In particular, we conclude that electron–electron interactions cause only minor changes to the FIR spectra and deviations from the Kohn modes result from the low-symmetry confinement potential.