Damped response theory description of two-photon absorption

Damped response theory is applied to the calculation of two-photon absorption (TPA) spectra, which are determined directly, at each frequency, from a modified damped cubic response function. The TPA spectrum may therefore be evaluated for selected frequency ranges, making the damped TPA approach attractive for calculations on large molecules with a high density of states, where the calculation of TPA using standard theory is more problematic. Damped response theory can also be applied to the case of intermediate state resonances, where the standard TPA expression is divergent. Both exact damped response theory and its application within density functional theory are discussed. The latter is implemented using an atomic-orbital based density matrix formulation, which makes the approach especially suitable for studies on large systems. A test preliminary study is presented for the TPA spectrum of R-(+)-1,1'-bi(2-naphtol).     

Variational response-function formulation of vibrational circular dichroism

The atomic axial tensor (AAT) of vibrational circular dichroism is expressed as the frequency derivative at zero frequency of a linear response function for operators referencing a nuclear displacement and a magnetic field. This is used in the density matrix-based quasienergy derivative Lagrangian approach of Thorvaldsen et al. [J. Chem. Phys., 2008, 129, 214108] to express the AAT in a form where the need to solve response equations for the nuclear displacements is removed, significantly reducing the computation cost compared to existing formulations. The density matrix-based quasienergy derivative Lagrangian approach also allows us straightforwardly to use London atomic orbitals to remove the gauge-origin dependence and to account for the atomic orbitals' dependence on the nuclear coordinates. The formalism is entirely based on atomic-orbital density and integral matrices and therefore amenable to linear scaling for sufficiently sparse matrices and given a linearly scaling response solver.     

Voltammetry and in situ scanning tunnelling spectroscopy of osmium, iron, and ruthenium complexes of 2,2':6',2'-terpyridine covalently linked to Au(111)-electrodes

We have studied self-assembled molecular monolayers (SAMs) of complexes between Os(II)/(III), Fe(II)/(III), and Ru(II)/(III) and a 2,2',6',2'-terpyridine (terpy) derivative linked to Au(111)-electrode surfaces via a 6-acetylthiohexyloxy substituent at the 4'-position of terpy. The complexes were prepared in situ by first linking the terpy ligand to the surface via the S-atom, followed by addition of suitable metal compounds. The metal-terpy SAMs were studied by cyclic voltammetry (CV), and in situ scanning tunnelling microscopy with full electrochemical potential control of substrate and tip (in situ STM). Sharp CV peaks were observed for the Os- and Fe complexes, with interfacial electrochemical electron transfer rate constants of 6-50 s(-1). Well-defined but significantly broader peaks (up to 300 mV) were observed for the Ru-complex. Addition of 2,2'-bipyridine (bipy) towards completion of the metal coordination spheres induced voltammetric sharpening. In situ STM images of single molecular scale strong structural features were observed for the osmium and iron complexes. As expected from the voltammetric patterns, the surface coverage was by far the highest for the Ru-complex which was therefore selected for scanning tunnelling spectroscopy. These correlations displayed a strong peak around the equilibrium potential with systematic shifts with increasing bias voltage, as expected for a sequential two-step in situ ET mechanism.     

Finding the Hamiltonian for Cosmological Models in Fourth-Order Gravity Theories Without Resorting to the Ostrogradski or Dirac Formalism

The Hamilton formalism of cosmological models in fourth-order theories of gravity is considered. An approach to constructing the Hamilton function is presented which starts by replacing the second order derivatives of configuration space coordinates by functions depending on these coordinates, its first order derivatives, and additional variables playing the role of configuration space coordinates. This formalism, which does not resort to the Ostrogradski or Dirac formalism, is elucidated and applied to examples. For a special class of Lagrange functions, it is demonstrated that the canonical coordinates of the considered formalism and of the Ostrogradski formalism are related via a canonical transformation. The canonical transformation is a transformation of the configuration space coordinates and a transformation of momentum components induced by the transformation of the configuration space coordinates for a special element of the class of Lagrange functions mentioned. The Wheeler-DeWitt equations belonging to this Lagrange function are related via minisuperspace coordinate transformations.     

On the Interaction of Fermion and Boson Fields with the Gravitational Field

We point out that the gravitational field taken by itself cannot be considered as a gauge field. Only an affinity and not a metric can serve as a gauge field. Originally, metric and affinity are completely independent of each other. This fact allows in a natural way to formulate a restricted principle of relativity, according to which only fermion fields may show that there exist a priori distinguished frames of reference. Furthermore, we can couple the gravitational field to boson and fermion fields such that the flat metric or tetrads orthonormalized with respect to this flat metric appearing in the special relativistic matter Lagrangian, are replaced by a Riemannian metric and tetrads orthonormalized with respect to this metric (principle of most minimal gravitational coupling). This coupling principle is a strong restriction on the existence of independent boson fields. Only scalar and vector fields and their different pseudoquantities are possible as independent fields. Boson fields of higher rank are to be considered as fusions of these (pseudo)scalar and (pseudo)vector fields. Theire field equations follow from those of the (pseudo)scalar and (pseudo)vector fields.     

Fermion Fields,Boson Fields,and Gravitational Field

If a tetrad theory is derivable from a variational principle with a Lagrangian ?? of the form ?? = ??_F+??_M 6 tetrad components will be defined by the vacuum equations if the energy momentum tensor is symmetric. Therefore, we look for a realisation of a programme proposed in a little different way by TREDER according to which the 16 tetrad field equations should degenerate to 10 equations for the Riemannian metric if boson fields are the only source of the gravitational field.     

Interparticle forces in silica nanoparticle agglomerates

To improve the understanding of the poor dispersability of fumed silica nanoparticle agglomerates, the stability of highly defined agglomerated model particles was investigated. The high temperature synthesis conditions for fumed silica were simulated by tempering. Along with electron-microscopical analysis of the sintering necks, the interparticle forces were investigated by energy resolved fragmentation analysis based on low pressure impaction. At temperatures above 1,000 °C the fragmentability of the agglomerates rapidly decreased while the energy necessary for fragmentation increased. The development of sintering necks was observed for temperatures exceeding 1,300 °C. Comparison of the experimental data with the fragmentation behaviour of a commercially produced fumed silica indicated solid state contacts (sintering necks) as being most numerous in the agglomerates resulting in limited fragmentability.     

基于锗硅芯片的光电子学前景与挑战

作为微电子材料,硅具备许多优良的电学特性．采用硅材料的器件集成度能够比其他材料高几个数量级。然而．硅是一种间接带隙材料,其光学跃迁过程会引入大量低能的声子造成跃迁几率很低．导致其光学特性（发射与吸收）远不如Ⅲ/Ⅴ族半导体材料。     

No Arbitrage and the Growth Optimal Portfolio

Abstract

Recently, several papers have expressed an interest in applying the Growth Optimal Portfolio (GOP) for pricing derivatives. We show that the existence of a GOP is equivalent to the existence of a strictly positive martingale density. Our approach circumvents two assumptions usually set forth in the literature: 1) infinite expected growth rates are permitted and 2) the market does not need to admit an equivalent martingale measure. In particular, our approach shows that models featuring credit constrained arbitrage may still allow a GOP to exist because this type of arbitrage can be removed by a change of numéraire. However, if the GOP exists the market admits an equivalent martingale measure under some numéraire and hence derivatives can be priced. The structure of martingale densities is used to provide a new characterization of the GOP which emphasizes the relation to other methods of pricing in incomplete markets. The case where GOP denominated asset prices are strict supermartingales is analyzed in the case of pure jump driven uncertainty.