Structure of adsorbed organometallic rhodium: model single atom catalysts

We have determined the structure of a complex rhodium carbonyl chloride [Rh(CO)(2)Cl] molecule adsorbed on the TiO2 (110) surface by the normal incidence x-ray standing wave technique. The data show that the technique is applicable to reducible oxide systems and that the dominant adsorbed species is undissociated with Rh binding atop bridging oxygen and to the Cl found close to the fivefold coordinated Ti ions in the surface. A minority geminal dicarboryl species, where Rh-Cl bond scission has occurred, is found bridging the bridging oxygen ions forming a high-symmetry site

Levinson's Theorem for Non-local Interactions in Two Dimensions

In the light of the Sturm-Liouville theorem, the Levinson theorem for the Schr\"{o}dinger equation with both local and non-local cylindrically symmetric potentials is studied. It is proved that the two-dimensional Levinson theorem holds for the case with both local and non-local cylindrically symmetric cutoff potentials, which is not necessarily separable. In addition, the problems related to the positive-energy bound states and the physically redundant state are also discussed in this paper.Comment: Latex 11 pages, no figure, submitted to J. Phys. A Email: [email protected], [email protected]

Levinson's theorem for the Schr\"{o}dinger equation in two dimensions

Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically symmetric potential in two dimensions is re-established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison with Levinson's theorem in non-critical case, the half bound state for $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of $P$ wave at zero energy to increase an additional $\pi$.Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email: [email protected], [email protected]

Completeness of the Coulomb scattering wave functions

Completeness of the eigenfunctions of a self-adjoint Hamiltonian, which is the basic ingredient of quantum mechanics, plays an important role in nuclear reaction and nuclear structure theory. However, until now, there was no a formal proof of the completeness of the eigenfunctions of the two-body Hamiltonian with the Coulomb interaction. Here we present the first formal proof of the completeness of the two-body Coulomb scattering wave functions for repulsive unscreened Coulomb potential. To prove the completeness we use the Newton's method [R. Newton, J. Math Phys., 1, 319 (1960)]. The proof allows us to claim that the eigenfunctions of the two-body Hamiltonian with the potential given by the sum of the repulsive Coulomb plus short-range (nuclear) potentials also form a complete set. It also allows one to extend the Berggren's approach of modification of the complete set of the eigenfunctions by including the resonances for charged particles. We also demonstrate that the resonant Gamow functions with the Coulomb tail can be regularized using Zel'dovich's regularization method.Comment: 12 pages and 1 figur

The gravitational S-matrix

We investigate the hypothesized existence of an S-matrix for gravity, and some of its expected general properties. We first discuss basic questions regarding existence of such a matrix, including those of infrared divergences and description of asymptotic states. Distinct scattering behavior occurs in the Born, eikonal, and strong gravity regimes, and we describe aspects of both the partial wave and momentum space amplitudes, and their analytic properties, from these regimes. Classically the strong gravity region would be dominated by formation of black holes, and we assume its unitary quantum dynamics is described by corresponding resonances. Masslessness limits some powerful methods and results that apply to massive theories, though a continuation path implying crossing symmetry plausibly still exists. Physical properties of gravity suggest nonpolynomial amplitudes, although crossing and causality constrain (with modest assumptions) this nonpolynomial behavior, particularly requiring a polynomial bound in complex s at fixed physical momentum transfer. We explore the hypothesis that such behavior corresponds to a nonlocality intrinsic to gravity, but consistent with unitarity, analyticity, crossing, and causality.Comment: 46 pages, 10 figure

Relation between the separable and one-boson-exchange potential for the covariant Bethe-Salpeter equation

We investigate the relation between the rank I separable potential for the covariant Bethe-Salpeter equation and the one-boson-exchange potential. After several trials of the parameter choices, it turns out that it is not always possible to reproduce the phase-shifts calculated from a single term of the one-boson-exchange potential especially of the $\sigma$-exchange term, separately by the rank I separable potential. Instead, it is shown that the separable potential is useful to parameterize the total nucleon-nucleon interaction.Comment: 10 pages, 8 figures, to appear in J.Phys.

Influence of branch points in the complex plane on the transmission through double quantum dots

We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S-matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. This model allows to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.Comment: 30 pages, 14 figure

Completeness of evanescent modes in layered dielectrics

In the presence of a dielectric slab, the modes of the free electromagnetic field comprise traveling modes, consisting of incoming, reflected, and transmitted parts, as well as trapped modes that are subject to repeated total internal reflection and emerge as evanescent field outside the slab. Traveling modes have a continuous range of frequencies, but trapped modes occur only at certain discrete frequencies. We solve the problem of which relative weight to use when summing over all modes, as commonly required in perturbative calculations. We demonstrate the correctness of our method by showing the completeness of electromagnetic field modes in the presence of a dielectric slab. We derive a convenient method of summing over all modes by means of a single contour integral, which is very useful in standard quantum electrodynamic calculations

Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

Analytic results are derived for the apparent slip length, the change in drag and the optimum air layer thickness of laminar channel and pipe flow over an idealised superhydrophobic surface, i.e. a gas layer of constant thickness retained on a wall. For a simple Couette flow the gas layer always has a drag reducing effect, and the apparent slip length is positive, assuming that there is a favourable viscosity contrast between liquid and gas. In pressure-driven pipe and channel flow blockage limits the drag reduction caused by the lubricating effects of the gas layer; thus an optimum gas layer thickness can be derived. The values for the change in drag and the apparent slip length are strongly affected by the assumptions made for the flow in the gas phase. The standard assumptions of a constant shear rate in the gas layer or an equal pressure gradient in the gas layer and liquid layer give considerably higher values for the drag reduction and the apparent slip length than an alternative assumption of a vanishing mass flow rate in the gas layer. Similarly, a minimum viscosity contrast of four must be exceeded to achieve drag reduction under the zero mass flow rate assumption whereas the drag can be reduced for a viscosity contrast greater than unity under the conventional assumptions. Thus, traditional formulae from lubrication theory lead to an overestimation of the optimum slip length and drag reduction when applied to superhydrophobic surfaces, where the gas is trapped