The Ithaca interpretation of quantum mechanics

I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and discuss two simple recent theorems which have important implications for such an interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)     

Modeling plane turbulent Couette flow

Among the salient features of shear-driven plane Couette flow is the constancy of the total shear stress (viscous and turbulent) across the flow. This constancy gives rise to a quasi-homogenous core region, which makes the bulk of the flow substantially different from pressure-driven Poiseuille flow. The present second-moment closure study addresses the conflicting hypotheses relating to turbulent Couette flow. The inclusion of a new wall-proximity function in the wall-reflection part of the pressure-strain model seems mandatory, and the greement with recent experimental and direct numerical simulation (DNS) results is encouraging. Analysis of model computations in the range 750 ≤ Re ≤ 35,000 and comparisons with low-Re DNS data suggest that plane Couette flow exhibits a local-equilibrium core region, in which anisotropic, homogeneous turbulence prevails. However, the associated variation of the mean velocity in the core, as obtained by the model, conflicts with the intuitively appealing assumption of homogeneous mean shear. The constancy of the velocity gradient exhibited by the DNS therefore signals a deficiency in the modeled transport equation for the energy dissipation rate.     

Evolution of stress and strain relaxation of Ge and SiGe alloy films on Si(0 0 1)

The growth of Ge and SiGe alloy films on Si substrates has attracted considerable interest in the last years because of their importance for optoelectronic devices as well as Si-based high speed transistors. Here we give a short overview on our recent real time stress measurements of Ge and SiGe alloy films on Si(0 0 1) performed with a sensitive cantilever beam technique and accompanied by structural investigations with atomic force microscopy. Characteristic features in the stress curves provide detailed insight into the development and relief of the misfit strain. For the Stranski–Krastanow system Ge/Si(0 0 1) as well as for SiGe films with Si contents below 20%, the strain relaxation proceeds mainly into two steps: (i) by the formation of 3D islands on top of the Ge wetting layer; (ii) via misfit dislocations in larger 3D islands and upon their percolation.     

Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

Exact solutions and geometric phase factor of time-dependent three-generator quantum systems

There exist a number of typical and interesting systems and/or models, which possess three-generator Lie-algebraic structure, in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras are either isomorphic to the algebra sl (2, C) or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains exact solutions of the time-dependent Schr?dinger equations governing various three-generator Lie-algebraic quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown that the exact solutions can also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator (i.e., the time-independent invariant that commutes with the time-dependent Hamiltonian). The topological property of geometric phase factors and its adiabatic limit in time-dependent systems is briefly discussed. Received 6 July 2002 / Received in final form 21 October 2002 Published online 11 February 2003     

On the Donor Ability of the Phosphaneiminato Substituent and Cube Formation with Transition Metal Fragments

The particular role of the phosphaneiminato ligand as a donor is investigated for a) nitrenes (phosphinidenes) and carbenes and b) cubane formation with transition metals. Accordingly, and as shown for the case a) the ligand is a stronger π‐donor than an amino group and can be considered as a special case of imine‐type substituents. The latter are very effective in π‐donation. In the case b), i.e. the cubane formation with transition metals, one has to consider transition metals with a partially or completely filled d‐shell (with electrons). Hence depending on the transition metal, cubanes are build with weak ferromagnetic coupled or closed shell systems. For the cubanes with closed shell character the matter of insertion of halide anions is discussed. In the last chapter of the review the bond stretching in the dithionitrosyl complexes with rhenium is characterized.     

四能级原子系统中量子相干增强的Kerr非线性效应的研究

应用密度矩阵方程计算了四能级原子系统中三阶非线性极化率随信号光和探针光频率失谐的变化关系。结果表明，由于量子干涉对信号光强度的敏感性，使四能级原子介质的交叉Kerr非线性作用大大增强，与三能级系统相比，四能级原子介质的Kerr非线性系数可增强两个数量级。     

卤代对苝醌类光敏剂光敏活性影响的量子化学研究

以一种新型的醌类光敏剂—菌生素 (HMB)为模型化合物 ,利用量子化学从头算HF/ 6 31G和含时密度泛函TD B3LYP/ 6 31G方法计算研究了卤代作用对醌类光敏剂分子性质和光敏活性的影响 .结果发现 ,卤代作用降低了HMB母体的HOMO和LUMO能级 (EHOMO和ELUMO)及其差值△E ,随卤族元素从上到下 ,EHOMO和ELUMO呈增大趋势 ,而△E呈减小趋势 ,使得分子激发光谱有不同程度的红移 ,在增加PQP三重态量子产率的同时降低了分子最低三重激发态的能量 ,两种作用相互抵消 ,使得卤代物的 1O2 量子产率与母体相似 ;增加了分子的绝热电子亲合势 ,使分子产生O2 -的能力下降 ;卤原子的引入 ,降低了HMB母体分子内氢键的强度 ,同时使顺式构型的分子内质子传递势垒增大 ,而使反式构型势垒减小 .