On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

量子算法的NMR实现方法

量子计算机是一种以量子耦合方式进行信息处理的装置[1 ] 。原则上 ,它能利用量子相干干涉方法以比传统计算机更快的速度进行诸如大数的因式分解、未排序数据库中的数据搜索等工作[2 ] 。建造大型量子计算机的主要困难是噪音、去耦和制造工艺。一方面 ,虽然离子陷阱和光学腔实验方法大有希望 ,但这些方法都还没有成功实现过量子计算。另一方面 ,因为隔离于自然环境 ,核自旋可以成为很好的“量子比特” ,可能以非传统方式使用核磁共振 (NMR)技术实现量子计算。本文介绍一种用NMR方法实现量子计算的方法 ,该方法能够用比传统方法少的步骤解决一个纯数学问题。基于该方法的简单量子计算机使用比传统计算机使用更少的函数“调用”判断一未知函数的类别。     

Ultraslow phonon-assisted collapse of tubular image states

We predict ultraslow collapse of “tubular image states” (TIS) on material surfaces. TIS are bound Rydberg-like electronic states formed at large distances (∼30 nm) from the surfaces of suspended circularly-symmetric nanowires, such as metallic C nanotubes. The states are formed in potential wells, resulting from a combination of the TIS-electron attraction to image charges in the nanotube and its centrifugal repulsion, caused by spinning around the tube. We demonstrate that TIS can collapse on the tube surface by passing their angular momentum l to circularly polarized flexural phonons excited in the tube. Our analysis shows that for highly detached TIS with l ? 6 the relaxation lifetimes are of the order of 10 ns-1 μs, while for l < 6 these lifetimes are reduced by several orders of magnitude.     

On a conjecture of Fefferman and Graham

In 1985, Fefferman and Graham have constructed a local embedding of an arbitrary real-analytic manifold, of odd dimension n, into a Ricci-flat manifold of dimension n+2 admitting a homothety. They conjectured that their result remains valid in even dimensions, if logarithms are allowed in the expansion of the metric. In this paper, we (i) prove that such expansions exist and converge and (ii) establish the degree of non-uniqueness of the solution in terms of the coefficients in the expansion.     

Zero Dissipative, Explicit Numerov-Type Methods for Second Order IVPs with Oscillating Solutions

New explicit, zero dissipative, hybrid Numerov type methods are presented in this paper. We derive these methods using an alternative which avoids the use of costly high accuracy interpolatory nodes. We only need the Taylor expansion at some internal points then. The method is of sixth algebraic order at a cost of seven stages per step while their phase lag order is fourteen. The zero dissipation condition is satisfied, so the methods possess an non empty interval of periodicity. Numerical results over some well known problems in physics and mechanics indicate the superiority of the new method.     

基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

Crystallization and morphology of poly(vinylidene fluoride)/poly(3‐hydroxybutyrate) blends. I. Spherulitic morphology and growth by polarized microscopy

The development of the poly(3‐hydroxybutyrate) (PHB) morphology in the presence of already existent poly(vinylidene fluoride) (PVDF) spherulites was studied by two‐stage solidification with two separate crystallization temperatures. PVDF formed irregular dendrites at lower temperatures and regular, banded spherulites at elevated temperatures. The transition temperature of the spherulitic morphology from dendrites to regular, banded spherulites increased with increasing PVDF content. A remarkable amount of PHB was included in the PVDF dendrites, whereas PHB was rejected into the remaining melt from the banded spherulites. When PVDF crystallized as banded spherulites, PHB could consequently crystallize only around them, if at all. In contrast, PHB crystallized with a common growth front, starting from a defined site in the interfibrillar regions of volume‐filling PVDF dendrites. It formed by itself dendritic spherulites that included a large number of PVDF spherulites. For blends with a PHB content of more than 80 wt %, for which the PVDF dendrites were not volume‐filling, PHB first formed regular spherulites. Their growth started from outside the PVDF dendrites but could later interpenetrate them, and this made their own morphology dendritic. These PHB spherulites melted stepwise because the lamellae inside the PVDF dendrites melted at a lower temperature than those from outside. This reflected the regularity of the two fractions of the lamellae because that of those inside the dendrites of PVDF was controlled by the intraspherulitic order of PVDF, whereas that from outside was only controlled by the temperature and the melt composition. The described morphologies developed without mutual nucleating efficiency of the components. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 873–882, 2003