几何量子计算和拓扑量子计算——整体性量子现象的新应用

本文概述介绍量子计算的最新进展:几何量子计算和拓扑量子计算,是初步入门的引论性质。作者从量子力学的整体性现象这一观点出发,阐述作为整体现象的量子力学几何相位(亚贝尔和非亚贝尔几何相位),量子体系的拓扑不变性质等的新应用,为先前一本著作[1]所阐述观点的新发展的补充。     

Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

Evolution of polarization singularities accompanied by avoided crossing in plasmonic system

The evolution of polarization singularities supported in a one-dimensional periodic plasmonic system is studied. The lateral inversion symmetry of the system, which breaks the in-plane inversion symmetry and up-down mirror symmetry simultaneously, yields abundant polarization states. A complete evolution process with geometry for the polarization states is traced. In the evolution, circularly polarized points (C points) can stem from 3 different processes. In addition to the previously reported processes occurring in an isolated band, a new type of C point appearing in two bands simultaneously due to the avoided band crossing, is observed. Unlike the dielectric system with a similar structure which only supports at-$\varGamma$ bound states in the continuum (BICs), accidental BICs off the $\varGamma$ point are realized in this plasmonic system. This work provides a new scheme of polarization manipulation for the plasmonic systems.     

Generalized Variational-Like Inequalities with Nonmonotone Set-Valued Mappings

In this paper, we introduce a new class of generalized variational-like inequalities involving a nonmonotone-type set-valued mapping which is more general than those in the known literature. By applying a KKM-type theorem established by the author, some existence theorems for the solutions to the class of generalized variational-like inequalities are proved in Hausdorff locally convex topological vector spaces.     

Exact topological analogs to orthoposets

An arbitrary orthoposet is shown to be isomorphic to , being a subbasis of a Hausdorff topological space satisfying 1) , 2) , and 3) every covering of by elements of possesses an at most 2-element subcovering. The couple turns out to be unique.

     

超线性奇异Neumann边值问题的非平凡解

利用拓扑度计算,研究了一类超线性奇异Neumann边值问题非平凡解的存在性,其中非线性项可变号且下方无界.     

Plasma sprayed alumina coatings for radiation detector development

Conventional design of radiation detectors uses sintered ceramic insulating modules. The major drawback of these ceramic components is their inherent brittleness. Ion chambers, in which these ceramic spacers are replaced by metallic components with plasma spray coated alumina, have been developed in our Research Centre. These components act as thin spacers that have good mechanical strength as well as high electrical insulation and replace alumina insulators with the same dimensions. As a result, the design of the beam loss monitor ion chamber for CAT could be simplified by coating the outer surface of the HT electrode with alumina. One of the chambers developed for isotope calibrator for brachytherapy gamma sources has its outer aluminium electrode (60 mm dia × 220 mm long) coated with 250 μ thick alumina (97%) + titania (3%). In view of potential applications in neutron-sensitive ion chambers used in reactor control instrumentation, studies were carried out on alumina 100 μ to 500 μ thick coatings on copper, aluminium and SS components. The electrical insulation varied from 10⁸ ohms to 10¹² ohms for coating thicknesses above 200 μ. The porosity in the coating resulted in some fall in electrical insulation due to moisture absorption. An improvement could be achieved by providing the ceramic surface with moisture-repellent silicone oil coating. Irradiation at Apsara reactor core location showed that the coating on aluminium was found to be unaffected after exposure to 10¹⁷ nvt fluence.     

Raman scattering of Ge dot superlattices

Self-organised Ge dot superlattices grown by molecular beam epitaxy of Ge and Si layers utilizing Stranski-Krastanov growth mode were investigated by Raman spectroscopy. An average size of Ge quantum dots was obtained from transmission electron microscopy measurements. The strain and interdiffusion of Ge and Si atoms in Ge quantum dots were estimated from the analysis of frequency positions of optical phonons observed in the Raman spectra. Raman scattering by folded longitudinal acoustic phonons in the Ge dot superlattices was observed and explained using of elastic continuum theory. Received 25 January 2000     

Mott transition in anharmonic confinement

Two effects are identified that affect the visibility of the Mott transition in an atomic gas in an optical lattice confined in a power-law potential. The transition can be made more pronounced by increasing the power law, but at the same time, experimental uncertainty in the number of particles will induce corresponding fluctuations in the measured condensate fraction. Calculations in two dimensions indicate that a potential slightly more flat-bottomed than a quadratic one is to be preferred for a wide range of particle number fluctuation size.     

拓扑缺陷的不同分布对单壁碳纳米管电学性能的影响

在紧束缚近似基础上,利用扩展的Su-Schriffer-Heeger(SSH)模型,在实空间研究了在完整的"zigzag"碳纳米管中分别引入5/7,5/6/7,5/6/6/7拓扑缺陷所构成的(9,0)-(8,0),(9,0)-(7,0)和(9,0)-(6,0)三种异质结的电学性能.通过研究表明:这些拓扑缺陷不仅改变碳管的直径,而且支配费米能级附近的电学行为.并计算了(9,0)-(8,0),(9,0)-(7,0)和(9,0)-(6,0)系统的电子态密度,对这3种异质结的能带结构和电子态密度进行了比较.结果表明:五边形和七边形在碳管中分布的不同对碳管电学性能的影响明显不同.因此,可以研制出基于这些异质结的不同的电子器件基元.