Polaronic Band Structure of Holstein Model

A new concise approach is presented for analytic study of the properties of the Holstein model. New analytic results for the polaronic band structure and phonon distribution, of the Holstein molecular crystal model, are given in one dimension. And all analytic results given are in accordance with the known numerical research results.

Derivative Form of Off-axis Aberration Correction Surface and Its Application in Solar Energy Concentration

由使用衍生物方法，我们与陈等的以前的工作的获得了一样的结果。在 2006。与不可分的表格不同，在这篇论文出版的表面表示的衍生物表格从微分方程被导出，基于非成像集中的理论，日光反射装置由陈等求婚了。在 2001。固定错误修正表面的衍生物表格的比较在集中太阳的光线象球形的表面的一样与不可分的表格表面的被做了。

Bosonic and Fermionic Entropy of (2+1)-Dimensional Charged Black Hole

From resolving Klein-Gordon equation and Dirac equation in (2+1)-dimensional charged black hole spacetime and using 't Hooft's boundary condition and "quasi-periodic" boundary condition in the thin film brick wall model of black hole, which is introduced by LIU Weng-Biao and ZHAO Zheng, we obtain the bosonic and fermionic entropy of (2+1)-dimensional charged black hole, and find that the bosonic entropy is three times of fermionic entropy.

Calculating the Relativistic Wave Functions of 11S0 and 13S1 Positronium

Based cn the relativistic Bethe-Salpeter (BS) equation, the positronium wavefunctions in Euclidean momentum space are obtained. Meanwhile the energy levels of positronium ground states 11S0 and 13S1 are fitted to be 6.7934 eV and 6.7929 eV respectively, which qualitatively agree with the previous theoretical values. It is shown that the BS theory is valid and reliable to treat positronium.

A Multiwavelength Study of the Jets in FR-I Radio Galaxies:I.Data and Analysis

We compile a sample of 11 Fanaroff-Riley type I Radio Galaxies （FR-I RGs） with multi-wavelength observations to address the dynamic behavior of jets in these objects. Optical images acquired by the Hubble Space Telescope （HST） are carefully analyzed. The method and reduction procedure are described in detail. Unresolved optical cores emerge after having properly removed starlight from the host galaxies in eight of the FR-I RGs, of which five are new identifications. Broad band spectral properties of these newly identified compact cores are compared with that previously found in FR-I RGs, as well as the low-energy-peaked BL Lac objects. The similarity between them argues for the same non-thermal synchrotron origin. Well-resolved optical jets with knotty morphologies are found in three FR-I RGs in our sample, namely 3C 15, 3C 66B and B2 0755＋37. The optical counterparts to the inner radio/X-ray jets are identified and a clear one-to-one correspondence between the optical, radio and X-ray knots is found. The structure and information on the optical jets are discussed. Physical parameters such as the knots position, flux and size are also presented. Detailed comparison between the multi-wavelength data and radiative and dynamic models of jet will be made in a forthcoming paper.

Silicon Purification by a New Type of Solar Furnace

We propose a new method to reveal a direct transformation from solar energy to solar electricity. Instead of using electricity in the process, we use concentrated solar rays with a crucibleless process to upgrade metallurgical silicon into solar-grade silicon feedstock.

Transport Properties of a Classical One-Dimensional Kicked Billiard Model

We study a classical 1-dimenslonal kicked billiard model and investigate its transport behavior. The roles played by the two system parameters a and K, governing the direction and strength of the kick, respectively, are found to be quite crucial. For the perturbations which are not strong, i.e. K<1, we find that as the phase parameter α changes within its range of interest from -π/2 to π/2, the phase space is in turn characterized by the structure of a prevalently connected stochastic web (-π/2 ≤α<0), local stochastic webs surrounded by a stochastic sea(0<α<α/2 ) and the global stochastic sea (α=π/2). Extensive numerical investigations also indicate that the system's transport behavior in the irregular regions of the phase space for K<1 has a dependence on the system parameters and the transport coetticient D can be expressed as D≈D0(α)Kf(α).For strong kicks, i.e. K >1, the phase space is occupied by the stochastic sea, and the transport behavior of the system seems to be similar to that of the kicked rotor and independent of α.

Realization of Tip Tilting By 8-Step Line Tilting

By direct calculation of rotation matrices of SO(3),we show how certain specific sequence of eight consecutiverotations of digital angles can yield a tilting of a facet mirror.We also design a detailed program specifically to tiltan array of mirrors from planar orientation to the required focusing orientation.We describe how to use the 8-step torealize the focusing of the mirror array.We have found,in our designed program,an important feature of row-sharingduring the rotations for the columns and similarly the column-sharing during the rotations for the row.This feature cansave a lot of operating time during the actual realization of the mechanical movements.

(2+1)-Dimensional AdS Black Hole in Grand Canonical Ensemble

We investigate thermodynamics of the (2+1)-dimensional AdS black hole in grand canonical ensemble. In the York's formalism, the black hole is enclosed in a "box" with a finite radius and the boundary temperature, radius and potential are fixed in the grand canonical ensemble. We investigate the thermodynamical properties such as action,entropy, temperature, etc. We only find the stable solution for (2+1)-dimensional AdS black hole and do not find the instanton with the negative heat capacity.

Digitalized Mirror Array and Its Application in Large Telescope:Principle and Case Studies

In this article,we report the principle and conceptual design of a fundamentally different technology infabricating high precision aberration free optical devices.The tip-tilt of facet in a mirror array is produced by digitallycontrolled line-tilts of rows and columns.It has not only provided a cost-effective designing methodology in opticalphysics but also led to a much finer precision of 1 mili arc sec or Jess.As examples of the application of the proposeddigitalised optics,two case studies have been given:a 10 m Schmidt telescope(off-axis)and an 8 m Cassegrain telescope(on-axis).

Anomalous Dimension in the Solution of a Nonlinear Diffusion Equation

A new method is used to obtain the anomalous dimension in the solution of the nonlinear diffusion equation.The result is the same as that in the renormalization group (RG) approach.It gives us an insight into the anomalous dimension in the solution of the nonlinear diffusion equation in the RG approach.Based on this discussion,we can see anomalous dimension appears naturally in this system.

Complete Solution of Sun Tracking for Heliostat

在地球上向一个任意地定位的目标为任意地面向的日光反射装置追踪的阳光的一个一般答案被出版。与太阳的追踪的公式的最一般的表格，这被看见使用的方位角举起，纺纱举起追踪公式等等。是它的特殊情况。在太阳能工程利用一般答案和它的意义的可能性被讨论。

Post-deposition dynamics of multiple cluster aggregation on liquid surfaces

A comprehensive simulation model--deposition, diffusion, rotation and aggregation--is presented to demonstrate the post-deposition phenomena of multiple cluster growth on liquid surfaces, such as post-deposition nucleation, post- deposition growth and post-deposition coalescence. Emphasis is placed on the relaxations of monomer density, dimer density and cluster density as well as combined cluster-plus-monomer density with time after deposition ending. It is shown that post-deposition coalescence largely takes place after deposition due to the large mobility of clusters on liquid surfaces, while the post-deposition nucleation is only possible before the saturation cluster density is reached at the end of the deposition. The deposition flux and the moment of deposition ending play important roles in the post-deposition dynamics.

Magnetic properties of tin-doped ferrites nanoparticles Sn_xFe_(3-x)O_4

Nanoparticles of tin-doped ferrites SnxFe3-xO4 (x=0, 0.1, 0.2, 0.3, 0.4, 1.0) were prepared by the precipitation exchange method. The particles of all specimens are crystalline with mean diameter in the range of 4-8 nm, and the lattice parameters enlarge with increasing tin content. Magnetization and Mssbauer data indicate that the specimens are paramagnetic. The saturation magnetization decreases, as well as the magnetization and the coercive field increase, with increasing tin-content, the possible causes of which were discussed.

Conservative Currents of Boundary Charges in AdS2+1 Gravity

The boundary charge which constitutes the Virasoro algebra in (2-+ 1)-dirnensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.

Manipulation of Nanoparticles Using Dark-Field-Illumination Optical Tweezers with Compensating Spherical Aberration

Based on our previous investigation of optical tweezers with dark field illumination [Chin. Phys. Left. 25（2008）329] nanoparticles at large trap depth are better viewed in wide field and real time for a long time, but with poor forces. Here we present the mismatched tube length to compensate for spherical aberration of an oil-immersion objective in a glass-water interface in an optical tweezers system for manipulating nanoparticles. In this way, the critical power of stable trapping particles is measured at different trap depths. It is found that trap depth is enlarged for trapping nanoparticles and trapping forces are enhanced at large trap depth. According to the measurement, 70-nm particles are manipulated in three dimensions and observed clearly at large appropriate depth. This will expand applications of optical tweezers in a nanometre-scale colloidal system.

Statistical Entropy of the Kaluza-Klein Black Hole from the Horizon Conformal Field Theory

The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge.It is shown that the entropy yielded by the standard Cardy formula agrees with the Bekenstein-Hawking entropy only if we take period T of function u as the periodicity of the Euclidean black hole.On the other hand,the first-order quantum correction to the entropy is proportional to logarithm of the Bekenstein-Hawking entropy with a factor-1/2.

Semiclassical Evaluation of the Quantum Propagator of Chaotic Systems

The propagators of quantum chaotic systems in configuration space are calculated semiclassically. For the strongly chaotic system whose phase space is torus, such as baker's map, we find that, long after a logarithm time, the quantum propagator can be evaluated approximately as the local average of the semiclassical one on each quantum cell h.

Calculation of the π Meson Electromagnetic Form Factor

The modified flat-bottom potential(MFBP)is given by the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviour of the effective quark-gluon coupling.Theπmeson electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson equation and Bethe-Salpeter equation in simplified impulse approximation(dressed vertex)with MFBP.All our numerical results give good fit to experimental values.

Two Theorems on Calculating the Relative Entropy of Entanglement

We present two theorems on calculating the relative entropy of entanglement.Theorem 1 is an extension of Vedral and Plenio's theorem(Phys.Rev.A 57(1998)1619)for pure states,which is useful for calculating the relative entropy of entanglement for all pure states as well as for a class of mixed states.Theorem 2 gives the relative entropy of entanglement for any bipartite state whose tripartite purification has two separable reduced bipartite states.