The general relativistic hydrogen atom

The general relativistic Dirac equation is formulated in an arbitrary curved space-time using differential forms. These equations are applied to spherically symmetric systems with arbitrary charge and mass. For the case of a black hole (with event horizon) it is shown that the Dirac Hamiltonian is self-adjoint, has essential spectrum the whole real line and no bound states. Although rigorous results are obtained only for a spherically symmetric system, it is argued that, in the presence of any event horizon there will be no bound states. The case of a naked singularity is investigated with the results that the Dirac Hamiltonian is not self-adjoint. The self-adjoint extensions preserving angular momentum are studied and their spectrum is found to consist of an essential spectrum corresponding to that of a free electron plus eigenvalues in the gap (–mc ², +mc ²). It is shown that, for certain boundary conditions, neutrino bound states exist.Supported in part by the National Science Foundation     

Radiation from accelerated impurities in a Bose-Einstein condensate

We investigate radiation spectra arising from accelerated point-like impurities in the homogeneous Bose-Einstein condensate. A general formula for the radiation spectrum is obtained in the integral form as a function of given impurity trajectory within the Bogoliubov approximation. The Planckian spectrum is obtained for a special accelerated motion, which is shown to be unphysical. Non-Planckian spectrum is found in the case of a uniformly accelerated impurity. We compare our result with similar settings discussed in other quantum systems.     

Application of the Lucy-Richardson deconvolution procedure to high resolution photoemission spectra

Angle-resolved photoemission has developed into one of the leading probes of the electronic structure and associated dynamics of condensed matter systems. As with any experimental technique the ability to resolve features in the spectra is ultimately limited by the resolution of the instrumentation used in the measurement. Previously developed for sharpening astronomical images, the Lucy-Richardson deconvolution technique proves to be a useful tool for improving the photoemission spectra obtained in modern hemispherical electron spectrometers where the photoelectron spectrum is displayed as a 2D image in energy and momentum space.     

"Green" noise in quasistationary stochastic systems

We consider the behavior of stochastic systems driven by noise with a zero value of spectral density at zero frequency ("green" noise). For this purpose we propose the version of the Krylov-Bogoliubov averaging method to study the systems which are not stationary in the case of an external white noise. We use the ergodicity of a nonlinear random function in the method, and obtain equations for any approximation of the theory. In particular, it is shown in the first approximation that there is an effective potential to describe the averaged motion of the system. We consider a phase-locked loop as an example and show that metastable states are possible. The lifetime of these states essentially increases if the form of a green noise spectrum becomes sharper in the low-frequency region. The high stability of the system driven by green noise is confirmed by numerical simulation. It is important that the theoretical result obtained by the averaging method and the one obtained in the simulation coincide with sufficient accuracy. In conclusion, we discuss some of the unsolved green noise problems. (c) 2001 American Institute of Physics.     

Extension of Planck's law of thermal radiation to systems with a steady heat flux

Planck's law of thermal radiation is limited to equilibrium systems that have a definite temperature and do not carry any heat flux. Here we extend it to steady‐state systems with a constant heat flux. The obtained formulas explicitly describe the spectrum of thermal radiation in every direction and provide a sound basis for the self‐consistent analysis of radiative heat transport across interfaces, gaps, layered and other important structures.     

On the Two-Dimensional Bragg Resonator

We derive systems of differential and integro-differential equations which allow one to correctly analyze eigenwaves and high-Q oscillations in coaxial systems with a weak two-period corrugation of the walls. The dispersion characteristics of the eigenwaves of a coaxial waveguide with such a corrugation are studied with allowance for the diffraction effects for the quasi-critical waves. In the case of the boundary-value problem with zero boundary conditions, which describes a specific type of coaxial resonators considered in [1], we obtain simplified formulas for the complex eigenfrequencies and Q-factors. The obtained expressions are indicative of the possible spectrum crowding of high-Q oscillations, which takes place as the longitudinal and/or transverse sizes of the resonator increase.     

受驱动光学系统多光子量子统计理论(Ⅱ)——劣腔情况

本文讨论在劣腔近似的情况下,受驱动光学系统多光子过程的FPE。并进行半经典线性稳定性分析。还讨论非经典效应,得出在双光子情况下,不同原子间的关联对非经典效应起着增强作用,这与单光子情况相反,也与良腔情况不同。文中求得双光子透射光谱,并得出双光子共振荧光光谱,其Rabi频率Ω∝y²(y为入射场)。 关键词：     

Bound and Scattering States of Extended Calogero Model with an Additional PT Invariant Interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameters differ from each other in the presence of PT invariant interaction.     

磁性金属材料中交换耦合作用和自旋波的研究

基于交换耦合理论通常使用的近似分析的一般原理, 严格的分析了没有特定假设情况下的磁序范围或有关磁化密度的形式, 及在任何近似下提出一种关于耦合参数的计算方法. 并结合铁磁系统(磁性金属材料Gd, Fe, Ni), 定量的讨论了这种关系的适用范围, 也对自旋波和交换耦合进行了相关分析. 分析表明: 对于近邻磁性原子之间的交换耦合的计算以及在有限波矢量情况下对自旋波谱的计算都得到较为有意义的改进. 提出的交换耦合近似及自旋波谱的关系, 应用于铁磁系统时对近邻原子之间相互作用能给出较好的描述, 或对任何磁体中非完全局域磁化的自旋波谱较大波矢部分给出较合理的描述. 从磁性理论来看, 按照本文模型应用于磁学系统计算得到的结果与实验结果较好的符合.     

Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time

We investigated the spatiotemporal modulation instability (MI) in a medium with a non-instantaneous Kerr response in which the nonlinear contribution to the refractive index is governed by a relaxing Debye type equation. The expression for the MI gain spectrum in non-instantaneous Kerr medium is obtained, which clearly reveals the influence of the finite time of the nonlinear response (relaxation effect) on the spatiotemporal MI. It is shown that, due to the relaxation effect, the spatiotemporal MI can appear for the case of anomalous dispersion and defocusing nonlinearity, while it cannot appear in instantaneous Kerr medium for the same case, and a new MI gain spectrum appears, adding to the conventional MI gain spectrum similar to that in an instantaneous Ker medium. In addition, the bandwidth of MI gain spectrum is extended and the maximum MI gain is reduced with increasing of the relaxation time. Interestingly, spatiotemporal MI can appear for any spatial frequencies in non-instantaneous Kerr medium for any combination of dispersion and nonlinearity. We have performed an experiment of MI in carbon disulfide (CS₂), a typical non-instantaneous Kerr medium, which shows quantitative agreement with the theoretical analyses.     

An alkali metal vapor laser amplifier

The operation of a transversely diode-pumped alkali metal vapor laser amplifier is theoretically studied. The amplifier operation is described by a rather intricate system of differential equations, which can be solved in the general case only numerically. In the case of intense incident radiation, an analytic solution is obtained which makes it possible to determine any energy characteristics of the laser amplifier and to find the optimal parameters of the active medium and pump radiation (temperature, buffer gas pressure, and intensity and width of the pump radiation spectrum).     

Signal identification in NMR spectra with coupled evolution periods

Novel multidimensional NMR experiments rely on modified time-domain sampling schemes to provide significant savings of experimental time. Several approaches are based on the coupling of evolution times resulting in a reduction of the dimensionality of the recorded spectra, and a concomitant saving of experimental time. We present a consistent and general tool, called EVOCOUP, for the analysis of these reduced dimensionality spectra. The approach is flexible in the sense that the input can consist of various forms of reduced dimensionality spectra, that any piece of information can be removed (provided enough information is left), e.g., signals undetectable due to poor signal-to-noise or covered by artifacts, and that it can be applied to spectra involving any number of nuclei. The use of a general optimization procedure and an appropriate target function provides for a robust approach with well-defined results and ensures optimal use of redundant information normally present in the input. Spectral overlap in the directly detected dimension is resolved in a fully automated manner, avoiding the assessment of signal quality and its use in combinatorial trials. The positions of all peaks in a corresponding full-dimensional spectrum are obtained without need for reconstruction of this spectrum. In a systematic analysis of a complete spectrum recorded for the 14 kDa protein azurin and involving five different nuclei, only four spin systems were missed and no false spins systems were detected.     

The influence of quantum interference effects on the resonance fluorescence spectra of a degenerate three-level atom

The resonance fluorescence spectra of a degenerate three-level atom of the V-type in the field of an intense monochromatic wave with an arbitrary polarization composition are investigated. Analytical expressions are derived for the resonance fluorescence spectra, and the angular distribution of spontaneous fluorescence of atoms is analyzed for the D-line emitted by vapors of alkali atoms. It is shown that the number of lines in the spectrum may decrease in the case of the linear polarization of spontaneous radiation. The radiation relaxation operator is obtained for the D-line of alkali metals in the case when an atom is near the metal surface. Interference effects for such systems are analyzed.     

Charged-boson fluid at zero-temperature in the fractional dimensional space

In the fractional dimensional space, the ground state properties of the charged-boson fluid are studied in a theory which goes beyond the random phase approximation by including correlations through a static local-field-factor. The structure factor and static local field-factor are obtained in the self-consistent method. Qualitative agreement with the Monte Carlo results on static screening is achieved by imposing self-consistency on the compressibility of the fluid in addition to self-consistency on the structure factor. Using the structure factors obtained in these methods, several properties of the charged boson system such as the energy spectrum of elementary excitations, the pair-correlation function, the ground state energy, the pressure, the chemical potential and the compressibility are obtained in several dimensions including both integer and fractional values. Results obtained in the later method in two and three dimensional systems are close to the Monte Carlo and hypernetted-chain methods. The Wigner crystallisation in the lower dimensional system is found at higher density of bosons. However, it vanishes in any lower dimensional system whose dimension lies below 2.     

The WKB method for the Dirac equation with the vector and scalar potentials

The WKB approximation is developed for the Dirac equation with the spherically symmetrical vector and scalar potentials. The relativistic wavefunctions are constructed, new quantization rule containing the spin-orbital interaction is obtained. For spherically symmetrical model of the Stark effect the quasi-classical spectrum of relativistic hydrogen-like atom is calculated. Application of the WKB method to the mass spectrum of the hydrogen-like quark systems was done.     

Nearest level spacing statistics in open chaotic systems: generalization of the Wigner surmise

We investigate the nearest level spacing statistics of open chaotic wave systems. To this end we derive the spacing distributions for the three Wigner ensembles in the one-channel case. The theoretical results give a clear physical meaning of the modifications on the spacing distributions produced by the coupling to the environment. Based on the analytical expressions obtained, we then propose general expressions of the spacing distributions for any number of channels, valid from weak to strong coupling. The latter expressions contain one free parameter. The surmise is successfully compared with numerical simulations of non-Hermitian random matrices and with experimental data obtained with a lossy electromagnetic chaotic cavity.     

Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback

In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.     

An exactly solvable model of a multidimensional incommensurate structure

The paper considers the class of Schrödinger multidimensional discrete operators with quasi-periodic unbounded potential for which essentially complete spectral analysis may be carried out. In the case of sufficiently high incommensurability of almost-periods, the spectrum of such operators is found to be pure point and simple, the eigenfunctions exponentially localized and the low frequency conductivity exponentially small. In the one-dimensional case, for any incommensurability, the spectrum does not contain the absolutely continuous component, while for small incommensurability the spectrum is singular continuous.     

受驱动光学系统多光子量子统计理论(Ⅲ)——绝热消除方法的改进

本文采用Lugiato的绝热消除方法讨论多光子理论。得出无论是良腔、还是劣腔情况其结果不仅包含了以前用Gordon绝热消除方法所得的,而且还能直接计算已被绝热消去的变量的关联,特别是在劣腔情况用两种方法计算得的场算符涨落的关联稳态值是不同的。由于Lugiato方法是自洽的,所以更为合理,在附录中还给出了劣腔情况多光子原子压缩公式及透射光谱公式。