Quantum confinement in an asymmetric double‐well potential through energy analysis and information entropic measure

Localization of a particle in the wells of an asymmetric double‐well (DW) potential is investigated here. Information entropy‐based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phase‐space area, are utilized to explain the contrasting effect of localization‐delocalization and role of asymmetric term in such two‐well potentials. In asymmetric situation, two wells behaves like two different potentials. A general rule has been proposed for arrangement of quasi‐degenerate pairs, in terms of asymmetry parameter. Further, it enables to describe the distribution of particle in either of the deeper or shallow wells in various energy states. One finds that, all states eventually get localized to the deeper well, provided the asymmetry parameter attains certain threshold value. This generalization produces symmetric DW as a natural consequence of asymmetric DW. Eigenfunctions, eigenvalues are obtained by means of a simple, accurate variation‐induced exact diagonalization method. In brief, information measures and phase‐space analysis can provide valuable insight toward the understanding of such potentials.     

Simultaneous two color image capture for sub-diffraction localization fluorescence microscopy

A sub-diffraction limit fluorescence localization microscope was constructed using a standard cooled 1.4 mega-pixel fluorescence charge-coupled device (CCD) camera to simultaneously resolve closely adjacent paired quantum dots on a flat surface with emissions of 540 and 630 nm. The images of the overlapping Airy discs were analyzed to determine the center of the point spread function after noise reduction using Fourier transformation analysis. The Cartesian coordinates of the centers of the point spread functions were compared in serial images. Histograms constructed from serial images fit well to Gaussian functions for resolving two quantum dots separated by as little as 10 nm in the x–y coordinates. Statistical analysis of multiple pairs validated discrimination of inter-fluorophore distances that vary by 10 nm. The method is simple and developed for x–y resolution of dilute fluorophores on a flat surface, not serial z sectioning.     

基于SLAM的连续运动测量坐标转换算法研究

本文基于同步定位与地图创建(Simultaneous Localization and Mapping,SLAM)原理,通过双目视觉系统的坐标转换方法,建立动态坐标系与静态基准点之间的关系,实现连续运动测量。通过实验,设计运动路线,验证坐标转换算法,并得到了建立在世界坐标系下的空间线形曲线。实验结果表明：转换后的坐标,x、y、z三个方向的最大误差不超过0.734mm。     

Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory

This article presents an overview of recent advances in the study of electron pairing through the use of localization and delocalization indices obtained from double integration over atomic basins of the exchange–correlation density in the framework of the atoms-in-molecules theory. These localization and delocalization indices describe the intra- and interatomic distribution of the electron pairs in a molecule. The main results of the application of these second-order indices to the analysis of molecular structure and chemical reactivity are briefly reviewed. It is shown that localization and delocalization indices represent a powerful tool to describe the electron-pair structure of molecules, which, in turn, provides deeper insight into relevant chemical phenomena such as electron correlation effects and the formation of localized α, β electron pairs. Received: 8 April 2002 / Accepted: 26 June 2002 / Published online: 6 September 2002 Acknowledgements. Financial help was furnished by the Spanish DGES projects no. PB98-0457-C02-01 and BQU2002-04112-C02-02. J.P. thanks the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya for benefiting from a doctoral fellowship, no. 2000FI-00582. M.S. is indebted to the Departament d'Universitats, Recerca i Societat de la Informació of the Generalitat de Catalunya for financial support through the Distinguished University Research Promotion, 2001. We also thank the Centre de Supercomputació de Catalunya for providing us with computing facilities. Correspondence to: M. Solà e-mail: miquel.sola@udg.es     

Anderson transition in dilute systems with pure exponential interactions

Summary Assuming a completely disordered lattice it is shown that all the states are localized when the disorder parameterx=a ₀/0 reachesthe value 0.31, wherea is the mean atomic separation anda ₀ is the Bohr radius.     

局部化函子的扩张问题

本文考虑了经典ｐ局部化函子在相应的范畴的最小正交偶扩张与最大正交偶扩张是否联系局部化函子的问题．这里ｐ是素数或零．     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Liquid-solid chromatography of diastereomers: Tetrasubstituted ethanes

Summary The separation by thin-layer chromatography (TLC) is reviewed for 25 pairs of tetrasubstituted-ethane diastereomers on silica. A total of 50 different mobile phases were used in order to define the basis of solvent selectivity for these separations. Separation factors (α) for various diastereomeric pairs are determined mainly by the relative localization of the strong solvent in these binary-solvent mobile phases (as measured by the mobile-phase parameter m). Relative retention of the diastereomers expressed by positive vs. negative values of α appear understandable on the basis of steric hindrance to adsorption and solvent-solute localization. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Localization for the evolution p-Laplacian equation with strongly nonlinear source term

In this paper we study the strict localization for the p-Laplacian equation with strongly nonlinear source term. Let u:=u(x,t) be a solution of the Cauchy problem

     

Hamiltonian map approach to 1D Anderson model

A one-dimensional diagonal tight binding electronic system is analyzed with the Hamiltonian map approach to study analytically the inverse localization length of an infinite sample. Both the uncorrelated and the dichotomic correlated random potential sequences are considered in the evaluations of the inverse localization length. Analytical expressions for the invariant measure or the angle density distribution are the main motivation of this work in order to derive analytical results. The well-known uncorrelated weak disorder result of the inverse localization length is derived with a clear procedure. In addition, an analytical expression for high disorder is obtained near the band edge. It is found that the inverse localization length goes to 1 in this limit. Following the procedure used in the uncorrelated situation, an analytical expression for the inverse localization length is also obtained for the dichotomic correlated sequence in the small disorder situation.