Sign of the quadrupole moment of proton drip-line nucleus 8B

The sign of the quadrupole coupling constant eqQ of ⁸B in ZrB₂ is determined to be positive through the β-delayed α-ray anisotropy measurement combined with the spin manipulation technique by use of the β-NMR. According to the theoretical calculation of the electric field gradient in ZrB₂, the sign of the quadrupole moment of ⁸B is deduced to be positive. This revised version was published online in August 2006 with corrections to the Cover Date.     

Classification of Hopf algebras of dimension 18

This paper contributes to the classification problems of finite dimensional Hopf algebras H over an algebraically closed field k of characteristic zero. It is shown that for a non-semisimple Hopf algebra H of dimension 18 either H or H* is pointed.     

Large-scale semidefinite programs in electronic structure calculation

It has been a long-time dream in electronic structure theory in physical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. Realization of the RDM approach has benefited greatly from recent developments in semidefinite programming (SDP). We present the actual state of this new application of SDP as well as the formulation of these SDPs, which can be arbitrarily large. Numerical results using parallel computation on high performance computers are given. The RDM method has several advantages including robustness and provision of high accuracy compared to traditional electronic structure methods, although its computational time and memory consumption are still extremely large. The work of Mituhiro Fukuda was primarily conducted at the Courant Institute of Mathematical Sciences, New York University.     

Dark resonance of Cs atoms velocity-selected in a thin cell

We carried out experimental and theoretical research on dark Raman resonances in the absorption of the probe monochromatic wave in a thin vapor cell, whose length is much less than the diameters of probe and coupling laser beams. In this case, only the slow atoms have enough time to settle down to the dark quantum state during a free flight between the end walls of the cell. As a result, a sub-Doppler structure is observed when one sweeps both the coupling and probe laser frequencies keeping the Raman resonance condition. Second harmonic lock-in detection is used to evaluate sharpness of the dark-resonance line. The cell-length dependence of the observed spectral profile is satisfactorily reproduced by the steady-state analysis of the density matrix in which the velocity-dependent transit time effect is taken into account.     

Behavior of Boron Implanted in Semiconductor Si

Using β-NMR with ¹²B nuclei the temperature dependence of the lattice locations of boron implanted in Si is studied. At low temperature almost 100% of the implanted B is in either substitutional site or nonsubstitutional site. Above 260 K, the nonsubstitutional B rapidly becomes undetectable and disappears at a temperature higher than 325 K due to the fast spin-lattice relaxation. Above 450 K, the fraction of substitutional B increases to 100%. These experimental results are consistently explained by the thermal atomic jump and the dissociation of the defect associated with the nonsubstitutional B. This revised version was published online in September 2006 with corrections to the Cover Date.     

Every non-Euclidean oriented matroid admits a biquadratic final polynomial

Richter-Gebert proved that every non-Euclidean uniform oriented matroid admits a biquadratic final polynomial. We extend this result to the non-uniform case.     

Weak Value,Quasiprobability and Bohmian Mechanics

We clarify the significance of quasiprobability (QP) in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov’s weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. We also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality.     

基于扫描电子显微镜的碳纳米管拾取操作方法研究

碳纳米管场效应管是未来纳米器件的发展方向,而制造纳米器件的前提是拾取碳纳米管,基于扫描电子显微镜(SEM)的微纳机器人操作系统能够实现碳纳米管拾取操作.本文建立拾取操作中碳纳米管与原子力显微镜(AFM)探针间范德瓦耳斯力力学模型,不同接触状态下范德瓦耳斯力越大越有利于拾取碳纳米管.在SEM视觉反馈图像中建立相对坐标系,首先提出倾角变值方法检测碳纳米管与AFM探针的接触状态,然后运用动态差值方法识别碳纳米管与AFM探针空间位姿并校正碳纳米管位姿,最后自下而上拾取碳纳米管.实验结果表明:拟合直线倾角变值较大时碳纳米管与AFM探针发生接触,动态差值变化为零时碳纳米管与AFM探针为空间线接触,在完全线接触模型下选择合适的接触角度、接触长度和拾取速度能够成功拾取碳纳米管.