Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians

We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered in the paper. An example taken from the literature is discussed in detail.     

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

POLYMERIZATION OF 1-BUTYL-2-TRIMETHYLSILYLACETYLENE BY TRANSITION METAL CATALYSTS

New silicon-containing disubstituted polyacetylene was prepared by the polymerization of BTMSA having two bulky substituents (n-butyl and trimethylsilyl) using transition metal catalysts. The polymerization proceeded in a mild manner and the final polymer yield was generally lower than those of silicon-containing monosubstituted acetylenes by the similar catalyst system. The characterization on the polymer structure revealed that the resulting poly(BTMSA) have a conjugated backbone system, but the polymers have peculiar copolymer composition of poly-(BTMSA) and poly(1-hexyne) due to the spontaneous desilylation during the polymerization. The fluoride-ion induced desilylation of poly(BTMSA) using n-Bu₄N⁺F^? in THF yielded a completely desilylated product, pure poly(1-hexyne).     

Construction of conformal mappings by generalized polarization tensors

We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Transition metal-free synthesis of primary amides from aldehydes and hydroxylamine hydrochloride

Primary aromatic amides can be synthesized from aldehydes and hydroxylamine hydrochloride in the presence of Cs₂CO₃. Various aromatic aldehydes (include some heteroaromatic aldehydes) are able to generate the corresponding aromatic amides in moderate to excellent yields.     

Neutral 1D Perovskite-Type ABX3 Phase Transition Material with a Narrowband Emission and Semiconductor Property

Cyclic organic amines are emerging as excellent building blocks to assemble organic–inorganic hybrid phase transition materials due to their flexible cyclic structure. Here, we have assembled a 1D organic-inorganic hybrid dielectric material C₅H₆NOPbBr₃ ( 1 ) by alloying the cyclic organic amine 3-hydroxypyridine. 1 displays a remarkable switchable dielectric response induced by an order-disorder transformation of the organic moiety, this transformation behaviour is confirmed by DSC and Hirshfeld surface measurements. More interestingly, 1 has a narrowband emission (FWHM=4.64 nm) at 590 nm; FWHM is a major quality figure for narrowband photodetectors. In addition, 1 exhibits semiconducting properties with an indirect bandgap of 2.78 eV by the analysis of the UV-Vis absorption results.     

Study on structure and properties of transition metal doped BiF3 by first-principles

Structure and physical properties of BiF₃ doped with M=Cr, Cu, Fe, Mn, Ni, Ti, V and Co are calculated by the DFT+U method. Effect of metal doping on the electronic structure and optical response of host materials BiF₃ is investigated systematically. New energy levels are formed and located within the band gap, which could decrease the recombination rate of e⁻/h⁺ pairs. Furthermore, transition metal doping extends the optical absorption of BiF₃ to the visible spectral region.     

同型二聚体肽模型的二维红外光谱

利用一个同型二聚体模型,甲酰胺二聚体,模拟一对肽基团.用量子化学从头计算考察了二聚体中酰胺-I带振动模式之间的振动耦合及其在空间的行为. 研究发现C=O伸缩振动耦合以静电作用为主,耦合有效距离能超过10 oA. 一维和二维红外光谱的激子模拟计算表明,耦合常数的空间依赖性能够清楚地表现在光谱特征中. 这些结果意味着多肽中C=O伸缩振动模式能够在很远的距离相互耦合并产生振动态的离域化.     

Chemical depth profiling and 3D reconstruction of III–V heterostructures selectively grown on non‐planar Si substrates by MOCVD

The chemical characterization of novel 3D architectures with nanometre‐scale dimensions is extremely challenging. The chemical composition of InGaAs/AlAs quantum wells selectively grown in SiO₂ trenches, 100–300 nm wide, is studied. Combining high lateral resolution 3D ToF‐SIMS analysis and Auger measurements, the chemical composition of individual trenches was obtained confirming the uniformity of these III–V heterostructures. These results correlate well with an average approach using SIMS depth profiling. The effects of ion beam orientation on the surface topography of confined structures were highlighted. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

关于《线性代数》教材改革的几点想法

随着现代科学技术的迅猛发展,尤其是计算机技术的广泛应用,我们应当在工科数学课程的教学内容、教学方法和教学手段上积极改革,与时俱进,以改进教学方法,提高教学质量,使得工科学生能借助于计算机,学好本专业所需的数学知识.在这篇短文中,我们想就《线性代数》的教学内容的改革