On Intermediate Subfactors of Goodman-de la Harpe-Jones Subfactors

In this paper we present a conjecture on intermediate subfactors which is a generalization of Wall’s conjecture from the theory of finite groups. Motivated by this conjecture, we determine all intermediate subfactors of Goodman-Harpe-Jones subfactors, and as a result we verify that Goodman-Harpe-Jones subfactors verify our conjecture. Our result also gives a negative answer to a question motivated by a conjecture of Aschbacher-Guralnick.     

A Weak Spectral Condition for the Controllability of the Bilinear Schrödinger Equation with Application to the Control of a Rotating Planar Molecule

In this paper we prove an approximate controllability result for the bilinear Schrödinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrödinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the controllability result to the density matrices. The proof is based on fine controllability properties of the finite dimensional Galerkin approximations and allows to get estimates for the L ¹ norm of the control. The general controllability result is applied to the problem of controlling the rotation of a bipolar rigid molecule confined on a plane by means of two orthogonal external fields.     

Effect of Quantum Fluctuation on Two-Dimensional Spatially Anisotropic Heisenberg Antiferromagnet with Integer Spin

In the present paper, we calculate the Gaussian correction to the critical value J_⊥^c caused by quantum spin fluctuation in a two-dimensional spatially anisotropic Heisenberg antiferromagnet with integer spin S. Previously, some authors computed this quantity by the mean-field theory based on the Schwinger boson representation of spin operators. However, for S=1, their result is much less than the one derived by numerical calculations. By taking the effect of quantum spin fluctuation into consideration, we are able to produce a greatly improved result.     

Prediction of propeller non-cavitation noise by superimposing shifted sound signal from an isolated blade

The time-cost of the propeller non-cavitation noise prediction can be greatly reduced by the isolated blade method,which is validated via hybrid URANS and acoustic analogy,followed by the acoustic characteristics of propeller in time domain are analyzed.Firstly,we predicted the sound of the E779 A propeller operating in uniform inflow and found a typical periodic characteristic of the sound pressure distribution on propeller blade as well as the sound signal of the receiver,and the result by the superimposing shifted sound signal from an isolated blade(isolated blade method) agreed well with the result by the integration on total blades,which validated the credibility of the isolated blade method in uniform inflow.Finally,we predicted the sound of a propeller running in the wake of submarine by the isolated blade method,and the result also agreed well with the result by the integration on total blades,which further indicated that the isolated blade method was also applicable for the non-cavitation noise prediction of the propeller running in non-uniform inflow.The noise prediction of the counter-rotating propeller,the pump-jet can also benefit from this method.     

中高能区电子与分子散射总截面的计算

实验表明,电子与分子碰撞总截面(TCS)与分子本身固有参数(极化率、键长等)有一定关系,所以可从理论上定量探索这种关系,找出包含这些参数的准经验公式 .理论上可根据散射截面的"低能极限为硬球势散射、高能极限为玻恩近似"的思想,参考实验上测得的一些分子的总截面与分子的极化率的定量关系,我们用分子的几何和物理参数模拟了一种准经验公式.?     

量子限制斯达克效应对三角形量子阱吸光特性的影响

本文通过计算量子力学波动方程以及载流子传输特性,哈密顿量的H能谱图和边界条件等的理论方法来分析量子限制斯达克效应对三角形量子阱体系吸收特性的影响,说明了选择合适的量子阱垒层对于提高三角形量子阱吸光率具有重要的意义。     

神光Ⅲ中退偏现象对系统隔离比的影响

通过离线实验指出了神光Ⅲ主机装置联机调试阶段中限制系统隔离比提高的主要因素来自于转角体结构中反射膜引入的退偏效应。从膜系理论出发建立了神光Ⅲ主机装置中的转角体结构的反射系数的计算模型,进而通过计算指出了退偏效应的主要来源是反射膜层厚度的偏差,然后通过数值计算与离线实验结果的对比确定了转角体结构中各个反射镜的反射系数。由此得到了转角体结构的总反射系数及其造成的神光Ⅲ主机装置系统隔离比的提升上限和进一步提升系统隔离比的思路。     

Ferromagnetism in an Itinerant Electron Cluster

In the present paper, we study the existence of metallic ferromagnetism in a cluster of nanometer scale, which is described by the Hubbard model defined on a complete graph. Therefore, the system is highly frustrated with respect to electron hopping. By solving the model exactly, we show that its ground state is fully spin-polarized at half-filling, even if the Coulomb interaction is finite. This conclusion is in sharp contrast to the well-known result for the Hubbard model on a bipartite lattice. As a result, our exact solution strongly suggests that frustration may play an important role in causing metallic ferromagnetism.     

Intertwining operator realization of non-relativistic holography

We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory (without specifying any action). Further we show that these operators and the bulk-to-boundary operators are intertwining operators. In analogy to the relativistic case, we show that each bulk field has two boundary fields with conjugated conformal weights. These fields are related by another intertwining operator given by a two-point function on the boundary. Analogously to the relativistic result of Klebanov–Witten we give the conditions when both boundary fields are physical. Finally, we recover in our formalism earlier non-relativistic results for scalar fields by Son and others.     

Information and information gain close to nonequilibrium phase transitions. Numerical results

Using a general result on the behavior of information and information gain close to instability points of self-organizing systems we calculate explicitly the information of a single order parameter close to a nonequilibrium phase transition. We also discuss by means of the result why the relevant quantities are interpreted as information rather than as entropy.     

Physics with nonperturbative quantum gravity: Radiation from a quantum black hole

We study quantum gravitational effects on black hole radiation, using loop quantum gravity. Bekenstein and Mukhanov have recently considered the modifications caused by quantum gravity on Hawking's thermal black-hole radiation. Using a simple ansatz for the eigenstates of the area, they have obtained the intriguing result that the quantum properties of geometry affect the radiation considerably, yielding a discrete spectrum, definitely non-thermal. Here, we replace the simple ansatz employed by Bekenstein and Mukhanov with the actual eigenstates of the area computed using loop quantum gravity. We derive the emission spectra, using a classic result in number theory by Hardy and Ramanujan. Disappointingly, we do not recover the Bekenstein-Mukhanov discrete spectrum, but — effectively — a continuum spectrum, consistent with Hawking's result. The Bekenstein-Mukhanov argument for the discreteness of the specrum is therefore likely to be an artifact of the ansatz, rather than a robust result (at least in its present kinematical version). The result is an example of concrete (although somewhat disappointing) application of nonperturbative quantum gravity.This essay received the second award from the Gravity Research Foundation, 1996—Ed.     

Mixed polarization in determining the film thickness of a silicon sphere by spectroscopic ellipsometry

The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a silicon sphere by ray tracking, we find that the sphere makes the parallel incident beam of the SE be divergent after reflection, and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory. By settling an aperture in front of the detector of the SE, we can almost eliminate the error. For the silicon sphere with a diameter of 94 mm used in the Avogadro project, the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method. The principle of the method and the results of the experimental verification are presented.     

Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. II. Phase diagram

This paper is the second part of our attempt of an extension of the Pirogov-Sinai theory of phase transitions at low temperatures, applicable to the lattice spin systems with finite range interactions, to the systems with infinite range interactions. Employing the cluster expansion method developed in Part I and modifying the notion of the truncated contour model introduced by Zahradnik, we extend the Pirogov-Sinai result on the structure of phase diagrams to our situations. As an application, we apply our result to Potts models with infinite range interactions.Work supported in part by the Basic Science Research Program, Ministry of Education, 1987     

Generating and enhancing lag synchronization of chaotic systems by white noise

In this paper, we study the crucial impact of white noise on lag synchronous regime in a pair of time-delay unidirectionally coupled systems. Our result demonstrates that merely via white-noise-based coupling lag synchronization could be achieved between the coupled systems (chaotic or not). And it is also demonstrated that a conventional lag synchronous regime can be enhanced by white noise. Sufficient conditions are further proved mathematically for noise-inducing and noise-enhancing lag synchronization, respectively. Additionally, the influence of parameter mismatch on the proposed lag synchronous regime is studied, by which we announce the robustness and validity of the new strategy. Two numerical examples are provided to illustrate the validity and some possible applications of the theoretical result.     

String theory and algebraic geometry of moduli spaces

It is shown how the algebraic geometry of the moduli space of Riemann surfaces entirely determines the partition function of Polyakov's string theory. This is done by using elements of Arakelov's intersection theory applied to determinants of families of differential operators parametrized by moduli space. As a result we write the partition function in terms of exponentials of Arakelov's Green functions and Faltings' invariant on Riemann surfaces. Generalizing to arithmetic surfaces, i.e. surfaces which are associated to an algebraic number fieldK, we establish a connection between string theory and the infinite primes ofK. As a result we conjecture that the usual partition function is a special case of a new partition function on the moduli space defined overK.     

Comments on upper bounds on the inflationary Hubble constant

This is a comment on a letter by Hawking establishing an upper bound on the value of the Hubble parameter during inflation. Here we show that his derivation of the result is based on an invalid mathematical approximation, and demonstrate that a similar bound can be obtained from the standard “slow-rollover” constraint. We also present a derivation of the same result that is completely independent of the form of the scalar field potential.     

A model of solidification under microgravity conditions

The influence of the microgravity environment on solidification processes is discussed. A simple model of the solidification of a binary-alloy is presented with the chemical diffusion influenced by the gravitational field. Using the results of Mullins and Sekerka, we employ the linear theory of hydrodynamic stability to investigate the interfacial instability driving the pattern-forming processes in solidification. As a result, we estimate the characteristic size of the elements of the emerging pattern. We show that, in spite of good agreement of our result with the size of cellulae observed in experiments, the model cannot explain the changes in the patterns occurring in space environment. In conclusion we shortly discuss the possibility of adding realism to our simple model by including the effect of convection.     

Electron Orbital Magnetic Moments in the Armchair Carbon Nanotubes

Based on the density functional theory, we calculate the band structure of an armchair carbon nanotube in an axial magnetic field. The result shows that there are two kinds of magnetic moments with different symmetries. One is the Aharonov--Bohm-type magnetic moment which can be easily understood with classical picture, the other belonging to the valence, and conduction sub-bands should be explained by quantum mechanics. We use an effective mass model to analyse the magnetic moments and by comparing with the result of first-principle calculation, we conclude that the effective mass model is reasonable to estimate the change of the band gap in magnetic fields.     

Gravitational interaction of two spinning particles in general relativity. II

Within the framework of the previous paper, we complete the set of equations of motion by including the spin propagation equation at first order. We check this equation with the known result on the precession, which is obtained by means of slow motion approximation of our result. A new scheme of expanding equations of motion is also introduced. It will be useful to undertake higher-order calculations.     

反馈方法在离子阱Doppler冷却中的应用研究

离子阱中离子的快速有效冷却在量子信息处理、光频标等领域都有重要的意义.基于Steixner 等提出的量子反馈模型,将反馈方法应用于离子的Doppler冷却.首先理论分析了该模型下离子运动信息的获取方式以及反馈对离子运动的影响,并推导出了存在反馈时离子运动所满足的方程,然后进行了仿真计算. 计算结果表明,利用量子反馈可以明显的提高离子冷却速率.还分析了反馈参数对离子冷却效率的影响. 关键词： 离子阱 Doppler冷却 量子反馈