Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint

We compute the cyclic homology of the coordinate ring A(SL_q(2)) of the quantum algebraic group SL _q (2). We observe a degeneration of the noncommutative de Rham complex. The results are also verified from the point of view of Connes' noncommutative differential geometry.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

硅酸盐中桥联键的机制及其性质的CNDO/2法研究

法计算模型,分析了桥联键的成键机制,解释了硅酸盐的通常性质。以体系总能量随桥角变化关系,解释了硅酸盐矿物及沸石分子筛中桥角Si-O-T出现的范围和几率。 由计算结果还发现,桥氧上具有较高的非键p-电子电荷Q_o~n,并随桥氧的第三配原子性质和距离R(M-O~(br))而变化,使桥氧具有授受电子的双重性质。在此基础上,探讨了沸石分子筛的碳离子催化活性机理,提出了锁与匙匹配原子对的催化活性中心的新观点。     

Temperature Development of Homo- and Hetero-Clustering in Saturated Vapors

Computational findings of temperature increase of clustering degree in saturated vapors are analyzed. A thermodynamic proof is presented and a simple criterion derived. Illustrations are based on saturated steam, magnesium and carbon vapor. The results are applicable to synthesis of fullerenes, metallofullerenes, and heterofullerenes, chemical vapor deposition technique, or atmospheric chemistry.     

2-三氰基乙烯基蒽及其旋转异构体的量子化学研究

用量子化学从头算方法 ,在RHF/STO - 3G水平上 ,对 2_三氰基乙烯基蒽 (2_TCVA)分子进行了理论计算 ,优化得到了它的平衡几何构型 ,并计算了它的谐振动频率 .结果表明 :2_TCVA存在两种旋转异构体 :2_TCVA(1)和 2_TCVA(2 ) ,2_TCVA(2 )的总能量比 2_TCVA(1)的略高 .在PM3/CIS水平上计算了它们的电子光谱 ,得到了由基态到各激发态的垂直跃迁能和相应的振子强度 .研究表明 :2_TCVA(1)和 2_TCVA(2 )的强度最大的吸收波长分别为 2 4 9.72nm和 2 89.4 1nm ,2_TCVA(2 )的强度最大的吸收波长比 2_TCVA(1)的要长 .计算结果与实验结果符合得较好     

Transition state geometry in radical abstraction reactions: comparison of interatomic distances in the intersecting parabolas and Morse curves models with quantum-chemical calculations

Interatomic distances in the transition state were estimated for the reactions of radical abstraction: H^· + H₂, H^· + HCl, H^· + CH₄, N^·H₂ + NH₃, HO^· + H₂O, HO₂ ^· + HOOH, and C^·H₃ + SiH₄. The calculation was performed by the quantum-chemical density functional method or coupled clusters method (QCH), as well as by the methods of intersecting parabolas (IPM) and Morse curves (IMM), using experimental data (activation energies and reaction enthalpies). The results of the latter two methods are close to the quantum-chemical calculation and differ only by the increment a: r(IPM or IMM) = a + r(QCH), where a = –4.5·10^–12 m for IPM and a = +1.9·10^–12 m for IMM.