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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
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
wave at zero energy to increase an additional .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 -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
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