Rationalization and the Gray index of phantom maps

In this paper we study a homotopy invariant of phantom maps called the Gray index. We give a new interpretation of the Gray index of a phantom map f:X→Y, in terms of the rationalization of X. We use this interpretation, in order to detect phantom maps of a specific Gray index. Finally, we examine the set of phantom maps with infinite Gray index in a tower theoretic way.     

内嵌水二聚体富勒烯(H2O)2@C84的基态性质与光谱特性

采用密度泛函B3LYP方法以6-31G为基组研究了富勒烯D_(2d)(23)-C_(84)和内嵌水二聚体富勒烯(H_2O)_2@D_(2d)(23)-C_(84)的中性、阴离子及阳离子基态几何结构、稳定性、电荷分布、能量、电偶极矩、能隙、红外及拉曼光谱特性;用含时的TD-B3LYP方法研究了富勒烯C_(84)和内嵌水二聚体富勒烯(H_2O)_2@C_(84)的紫外-可见吸收光谱.研究结果表明:水二聚体的加入导致了富勒烯分子的对称性降低、偶极矩增加,体系能隙减小,同时水二聚体的氢键键长减小.另外,水二聚体的加入改变了富勒烯分子的红外和拉曼光谱特征,如谐振频率的移动以及红外和拉曼峰的增强或减弱.研究结果显示水二聚体的加入致使富勒烯分子的最大激发波长发生红移,对其它激发波长的位置以及振子强度也产生影响,如光学活性(振子强度不为0)的激发态成为光学非活性(振子强度为0)的激发态或者光学非活性的激发态成为光学活性的激发态;同时研究发现C_(84)存在能量简并的激发态,而(H_2O)_2@C_(84)并没有能量简并的激发态;虽然水二聚体的加入影响富勒烯分子的激发特性,但计算结果显示C_(84)和(H_2O)_2@C_(84)经展宽后的紫外-可见光谱轮廓基本一致.该研究可以为将来的实验光谱测量提供理论依据,也可以为内嵌水二聚体富勒烯的合成和应用提供理论指导.     

Sagnac quantum key distribution over telecom fiber networks

We present a new concept for compensation of single mode fiber (SMF) birefringence effects in a Sagnac quantum key distribution (QKD) setup, based on a polarization control system and a polarization insensitive phase modulator. Our experimental data show stable (in regards to birefringence drift) QKD over 1550 nm SMF telecom networks in Sagnac configuration, using the BB84-protocol [C.H. Bennett, G. Brassard, in: Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Institute of Electrical and Electronic Engineers, New York, 1984, p. 175] with phase encoding. The achieved total Sagnac transmission loop distances were between 100 km and 150 km with quantum bit error rates (QBER) between 5.84% and 9.79% for the mean-photon-number μ = 0.1. The distances were much longer and rates much higher than in any other published Sagnac QKD experiments. We also show an example of our one-decoy state protocol implementations (for the 45 km distance between Alice and Bob, corresponding to the 130 km total Sagnac loop length), providing an unconditional QKD security. The measurement results have showed feasibility of QKD over telecom fiber networks in Sagnac configuration, using standard fiber telecom components.     

Aluminium adsorption on Ir(1 1 1) at a quarter monolayer coverage: A first-principles study

We present an ab initio density-functional study for aluminium adsorption on Ir(1 1 1) at high symmetry sites, namely, the fcc-, hcp-hollow, top and bridge sites. In each case, we calculate the atomic geometry, average binding energy, work function, and surface dipole moment at the coverage of 0.25 monolayer. We find the favourable structure to be Al at threefold hcp-hollow site, with a corresponding binding energy of 4.46 eV. We present and compare the electronic properties of the two lowest energy structures, i.e., at the threefold hollow sites and discuss the nature of the Al-Ir bond and binding site preference. In particular, we observe a large hybridization of Al-3s, 3p and Ir-5d states near Fermi level, forming an inter-metallic bonds. This results in a significant electron transfer from the Al atoms to the Ir(1 1 1) substrate, inducing an outward pointing surface dipole moment and a large decrease in the work function of 1.69 eV for Al in the hcp-hollow site. Compared to the fcc-hollow site, adsorption in the hcp-hollow site results in a lower density-of-states at the Fermi level, as well as a greater hybridization in the bonding states.     

Numerical calculations of the field-dependent magnetization of short rectangular prisms

A numerical iteration method is described for the calculation of the local magnetization on the surface of a short rectangular prism. The computed stray field of the prism is in good agreement with experimental results.     

Collective and single-electron interactions of electron beams with electromagnetic waves,and free-electron lasers

The field of radiation emission from electron beams is reviewed with special reference to work related to free-electron lasers. Different schemes of interaction in periodic structures, electromagnetic slow-wave structures, and in transverse confining force are distinguished. Various effects and devices such as traveling wave amplifiers, Smith-Purcell radiators, Cerenkov and bremsstrahlung-free electron lasers, cyclotron resonance masers, coherent bremsstrahlung and channeling radiation are discussed and the differences and relations among them are explained. A simple comprehensive model is developed to describe electron-beam interaction with an electromagnetic wave in periodic electromagnetic structures. The model is general enough to describe both collective and single-electron modes of interaction and quantum mechanical, classical and Fermi degenerate regimes. Simplified expressions are developed for the gain by stimulated emission of radiation and for gain conditions of the Smith-Purcell-Cerenkov type free-electron lasers under conditions of very thin electron beams and infinite interaction length. This research is supported by the Air Force Office of Scientific Research under contract AFOSR-76-2933     

A second-order perturbation method for potential calculations in non-homogeneous conducting layers

A second-order perturbation method is presented to calculate the influence of the non-homogeneous conductivity on the potential distribution in a conducting layer. The method is illustrated by resistance measurements on a rectangular geometry.     

Pulsed loop antennas

A rather simple and general analysis allows calculation of the transient response of many different radiators of practical interest directly in the time domain without the knowledge of the corresponding time harmonic field. Here, we present exact expressions for the transient near-and far-fields around thin circular current loops of arbitrary dimensions involving arbitrarily time-varying excitation. The resulting convolution integrals have been numerically evaluated for “step”-function currents with finite rise time, thus allowing interpretation of the different influence of small and large loops on the transient radiation field. The physical background of the time history of the ideal step-function response is discussed in detail. Dedicated to the 70th birthday of Prof. Dr.-Ing. habil. Gottfried Eckart.     

Generalized spherical and simplicial coordinates

Elementary trigonometric quantities are defined in l2,p analogously to that in l2,2, the sine and cosine functions are generalized for each p>0 as functions sinp and cosp such that they satisfy the basic equation p|cosp(φ)|+p|sinp(φ)|=1. The p-generalized radius coordinate of a point ξ∈Rn is defined for each p>0 as . On combining these quantities, ln,p-spherical coordinates are defined. It is shown that these coordinates are nearly related to ln,p-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on ln,p-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the ln,p-sphere and with the derivation of certain generalized statistical distributions.