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     

Click chemistry in materials synthesis. III. Metal‐adhesive polymers from Cu(I)‐catalyzed azide–alkyne cycloaddition

1,2,3‐Triazole‐based polymers generated from the Cu(I)‐catalyzed cycloaddition between multivalent azides and acetylenes are effective adhesive materials for metal surfaces. The adhesive capacities of candidate mixtures of azide and alkyne components were measured by a modified peel test, using a customized adhesive tester. A particularly effective tetravalent alkyne and trivalent azide combination was identified, giving exceptional strength that matches or exceeds the best commercial formulations. The addition of Cu catalyst was found to be important for the synthesis of stronger adhesive polymers when cured at room temperature. Heating also accelerated curing rates, but the maximum adhesive strengths achieved at both room temperature and high temperature were the same, suggesting that crosslinking reaches the same advanced point in all cases. Polytriazoles also form adhesives to aluminum, but copper is bound more effectively, presumably because active Cu(I) ions may be leached from the surface to promote crosslinking and adhesion. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5182–5189, 2007     

Deactivation reactions in the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated free‐radical polymerization of styrene: A comparative study with the 2,2,6,6‐tetramethyl‐1‐piperidinyloxy/acrylonitrile system

The competitiveness of the combination and disproportionation reactions between a 1‐phenylpropyl radical, standing for a growing polystyryl macroradical, and a 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO) radical in the nitroxide‐mediated free‐radical polymerization of styrene was quantitatively evaluated by the study of the transition geometry and the potential energy profiles for the competing reactions with the use of quantum‐mechanical calculations at the density functional theory (DFT) UB3‐LYP/6‐311+G(3df, 2p)//(unrestricted) Austin Model 1 level of theory. The search for transition geometries resulted in six and two transition structures for the radical combination and disproportionation reactions, respectively. The former transition structures, mainly differing in the out‐of‐plane angle of the N? O bond in the transition structure TEMPO molecule, were correlated with the activation energy, which was determined to be in the range of 8.4–19.4 kcal mol^?1 from a single‐point calculation at the DFT UB3‐LYP/6‐311+G(3df, 2p)//unrestricted Austin Model 1 level. The calculated activation energy for the disproportionation reaction was less favorable by a value of more than 30 kcal mol^?1 in comparison with that for the combination reaction. The approximate barrier difference for the TEMPO addition and disproportionation reaction was slightly smaller for the styrene polymerization system than for the acrylonitrile polymerization system, thus indicating that a β‐proton abstraction through a TEMPO radical from the polymer backbone could diminish control over the radical polymerization of styrene with the nitroxide even more than in the latter system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 232–241, 2007     

Nanostructured polymetallaynes of controlled length: Synthesis and characterization of oligomers and polymers from 1,1′‐bis‐(ethynyl)4,4′‐biphenyl bridging Pt(II) or Pd(II) centers

The reactivity of square planar palladium(II) and platinum(II) complexes in trans or cis configuration, namely trans or cis‐[dichlorobis(tributylphosphine)platinum(II)] and trans‐[dichlorobis(tributylphosphine)palladium(II)] with 1,1′‐bis(ethynyl) 4,4′‐biphenyl, DEBP, leading to π‐conjugated organometallic oligomeric and polymeric metallaynes, was investigated by a systematic variation of the reaction conditions. The formation of polymers and oligomers with defined chain length [? M(PBu₃)₂ (C?C? C₆H₄? C₆H₄? C?C? )]_n (n = 3–10 for the oligomers, n = 20–50 for the polymers) depends on the configuration of the precursor Pt(II) and Pd(II) complexes, the presence/absence of the catalyst CuI, and the reaction time. A series of model reactions monitored by XPS, GPC, and NMR ³¹P spectroscopy showed the route to modulate the chain growth. As expected, the nature of the transition metal (Pt or Pd) and the molecular weight of the polymers markedly influence the photophysical characteristics of the polymetallaynes, such as optical absorption and emission behavior. Polymetallaynes with nanostructured morphology could be obtained by a simple casting procedure of polymer solutions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3311–3329, 2007     

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 .     

Quantum Hall effect in back-gated InAs/GaSb heterostructures under a tilted magnetic field

We investigate the quantum Hall effect (QHE) in the InAs/GaSb hybridized electron–hole system grown on a conductive InAs substrate which act as a back-gate. In these samples, the electron density is constant and the hole density is controlled by the gate-voltage. Under a magnetic field perpendicular to the sample plane, the QHE appears along integer Landau-level (LL) filling factors of the net-carriers, where the net-carrier density is the difference between the electron and hole densities. In addition, longitudinal resistance maxima corresponding to the crossing of the extended states of the original electron and hole LLs make the QHE regions along integer-ν_net discontinuous. Under tilted magnetic fields, these R_xx maxima disappear in the high magnetic field region. The results show that the in-plane magnetic field component enhances the electron–hole hybridization and the formation of minigaps at LL crossings.