A Generalization of a Two-Parameter Quantization for the Group GL 2(k)

We generalize a well-known two-parameter quantization for the group GL ₂(k) (over an arbitrary field k). Specifically, a certain class of Hopf algebras is constructed containing that quantization. The algebras are constructed given an arbitrary coalgebra and an arbitrary pair of its commuting anti-isomorphisms, and are defined by quadratic relations. They are densely linked to the compact quantum groups introduced by Woronowicz. We give examples of Hopf algebras that can be rowed up to the two-parameter quantization for GL ₂(k).     

Photonic crystals--a step towards integrated circuits for photonics.

The field of photonic crystals has, over the past few years, received dramatically increased attention. Photonic crystals are artificially engineered structures that exhibit a periodic variation in one, two, or three dimensions of the dielectric constant, with a period of the order of the pertinent light wavelength. Such structures in three dimensions should exhibit properties similar to solid-state electronic crystals, such as bandgaps, in other words wavelength regions where light cannot propagate in any direction. By introducing defects into the periodic arrangement, the photonic crystals exhibit properties analogous to those of solid-state crystals. The basic feature of a photonic bandgap was indeed experimentally demonstrated in the beginning of the 1990s, and sparked a large interest in, and in many ways revitalized, photonics research. There are several reasons for this attention. One is that photonic crystals, in their own right, offer a proliferation of challenging research tasks, involving a multitude of disciplines, such as electromagnetic theory, nanofabrication, semi-conductor technology, materials science, biotechnology, to name a few. Another reason is given by the somewhat more down-to-earth expectations that photonics crystals will create unique opportunities for novel devices and applications, and contribute to solving some of the issues that have plagued photonics such as large physical sizes, comparatively low functionality, and high costs. Herein, we will treat some basics of photonic crystal structures and discuss the state-of-the-art in fabrication as well give some examples of devices with unique properties, due to the use of photonic crystals. We will also point out some of the problems that still remain to be solved, and give a view on where photonic crystals currently stand.     

A method and program for mass quantum chemical calculations of protein—ligand docking complexes

A new fast computational method for mass calculations of docking complexes by the AM1/PM3 semiempirical methods is proposed. The computation time is shortened by at least an order of magnitude compared to alternative schemes of quantum chemical calculations. The root-mean-square deviation of the AM1 calculated energies of formation of complexes from the results obtained by conventional diagonalization procedure is at most 0.4 kcal mol⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 418–420, February, 2008.     

Absorption measurement of strained SiGe nanostructures deposited by UHV-CVD

In order to obtain a low band gap photocell based on the widely spread silicon technology, e.g. for thermophotovoltaics, SiGe nanostructures can be introduced into a monocrystalline silicon photocell. Beforehand, it is necessary to know the absorption coefficient of the SiGe quantum wells. On a silicon (1 0 0) substrate multiple Si/SiGe quantum well structures were grown by UHV-CVD. The Ge concentration and the well width were used as growth parameters. To obtain significant absorption, the experiment was set up to allow for 200 internal reflections.The total reflection of the light results in a standing electromagnetic wave. The absorption coefficient was obtained from the experimental data taking the geometry and the electric field distribution in the absorbing layer into account. The influence of well width and germanium content on the absorption was investigated with the goal of maximizing the absorption for photons with energies below the band gap energy of silicon. The measurement results are compared with a theoretical model, which takes the band structure of strained SiGe including confinement effects into account.     

Path Integrals in Noncommutative Quantum Mechanics

We consider an extension of the Feynman path integral to the quantum mechanics of noncommuting spatial coordinates and formulate the corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians). The basis of our approach is that a quantum mechanical system with a noncommutative configuration space can be regarded as another effective system with commuting spatial coordinates. Because the path integral for quadratic Lagrangians is exactly solvable and a general formula for the probability amplitude exists, we restrict our research to this class of Lagrangians. We find a general relation between quadratic Lagrangians in their commutative and noncommutative regimes and present the corresponding noncommutative path integral. This method is illustrated with two quantum mechanical systems in the noncommutative plane: a particle in a constant field and a harmonic oscillator.     

Stress Tensor Fluctuations and Passive Quantum Gravity

The quantum fluctuations of the stress tensor of a quantum field are discussed, as are the resulting space-time metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the space-time geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.     

On Set-Theoretical Solutions to Quantum Yang-Baxter Equation

The problem on the set-theoretical solutions to the quantum Yang-Baxter equation was presented byDrinfel'd as a main unsolved problem in quantum group theory. The set-theoretical solutions are a natural extensionof the usual (linear) solutions. In this paper, we not only give a further study on some known set-theoretical solutions(the Venkov's solutions), but also find a new kind of set-theoretical solutions which have a geometric interpretation.Moreover, the new solutions lead to the metahomomorphisms in group theory.     

Hg1-xCdxTe/Cd1-zZnzTe的X射线反射率及半峰全宽的动力学研究

X射线衍射摇摆曲线的计算机模拟是一种获得材料晶体质量参量的有效方法，其中材料本征摇摆曲线的计算是计算机模拟的基础。用X射线动力学理论计算了Hg1-xCdxTe和Cd1-zZnzTe本征反射率曲线，并研究了组分、膜厚分别对本征反射率和半峰全宽的影响。结果表明Hg1-xCdxTe和Cd1-zZnzTe的本征反射率和半峰全宽与材料组分和厚度有明显的依赖关系，且该依赖关系取决于X射线在材料中的散射和吸收的相对强弱。薄膜的厚度也是直接影响本征摇摆曲线峰形、半峰全宽和反射率的重要因素，当薄膜厚度小于穿透深度时，表征本征反射率曲线的各个参量均与薄膜厚度有直接的关系。对于(333)衍射面，碲镉汞材料厚度大于7μm后，本征反射率和半峰全宽将不再发生明显变化。