Plasmon response of a quantum-confined electron gas probed by core-level photoemission

We demonstrate the existence of quantized "bulk" plasmons in ultrathin magnesium films on Si(111) by analyzing plasmon-loss satellites in core-level photoemission spectra, recorded as a function of the film thickness d. Remarkably, the plasmon energy is shown to vary as 1/d2 all the way down to three atomic layers. The loss spectra are dominated by the n=1 and n=2 normal modes, consistent with the excitation of plasmons involving quantized electronic subbands. With decreasing film thickness, spectral weight is gradually transferred from the plasmon modes to the low-energy single-particle excitations. These results represent striking manifestations of the role of quantum confinement on plasmon resonances in precisely controlled nanostructures.     

Hydrolysis of Cellobiose in Dilute Sulpuric Acid and Under Hydrothermal Conditions

The sulfuric acid hydrolysis rate of cellobiose between pH 2 and 3 is directly proportional to the acid concentration. In good agreement with other authors, an activation energy of 133 kJ/Mol was found under these acidic conditions. The relation of the reaction rate constants for the glucose formation and glucose degradation (k₁/k₂) shows, in contrast to the hydrolysis of cellulose, little dependence on the temperature. Hydroxymethylfurfural, and to a lesser extent furfural, are glucose degradation products, which are also consumed but at a lower reaction rate than glucose. At pH values between 3 and 4.7 (pure water) strong deviations of the hydrolysis rates were observed. The formation of organic acids decreases the pH but has no influence on the reaction rate. This fact indicates that hydrothermolysis follows a reaction mechanism different from that of acidic hydrolysis.     

General relativity as a conformally invariant scalar gauge field theory

The global symmetry implied by the fact that one can multiply all masses with a common constant is made into a local, gauge symmetry. The matter action then becomes Conformally invariant and it seems natural to choose for the corresponding scalar gauge field the action for a conformally invariant (massless) scalar field. The resulting conformally invariant theory turns out to be equivalent to general relativity. Since this means that the usual Einstein-Hilbert action is not, in fact, a true gauge action for the space-time geometry, the full theory ought to be supplied with such a term. Gauge-theoretic arguments and conformal invariance requirements dictate its form.     

Invariance identities associated with finite gauge transformations and the uniqueness of the equations of motion of a particle in a classical gauge field

A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the gauge potentials and their first derivatives, and also on certain gauge-dependent parameters whose properties are suggested by the interaction of an isotopic spin particle with a classical Yang-Mills field. It is shown that the necessary and sufficient conditions for the invariance of the given objects under a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a Lagrangian be gauge-invariant, uniquely determines the structure of these equations.     

Triplet-state optical spectra of highly concentrated isotopically mixed crystals of anthracene A-h10: A-d10

Photoexcitation spectroscopy with a dye laser is applied to study highly concentrated isotopically mixed crystals of anthracene A-h₁₀: A-d₁₀ in the region of the T₁ ← S_v 0-0 transition. The spectra of the separated A-h₁₀ and A-d₁₀ subbands are measured in polarized light at 6 K. The concentration-dependent intensities and energetic positions of the subbands are described quantitatively using the moment-expansion method of the mixed-crystal Green's function.     

Distributions of Points in <Emphasis Type="Italic">d</Emphasis> Dimensions and Large <Emphasis Type="Italic">k</Emphasis>-Point Simplices

We consider a variant of Heilbronn’s triangle problem by investigating for a fixed dimension d≥2 and for integers k≥2 with k≤d distributions of n points in the d-dimensional unit cube [0,1] ^d , such that the minimum volume of the simplices, which are determined by (k+1) of these n points is as large as possible. Denoting by Δ _k,d (n), the supremum of this minimum volume over all distributions of n points in [0,1] ^d , we show that c _k,d ⋅(log n)^1/(d−k+1)/n ^k/(d−k+1)≤Δ _k,d (n)≤c _k,d ′/n ^k/d for fixed 2≤k≤d, and, moreover, for odd integers k≥1, we show the upper bound Δ _k,d (n)≤c _k,d ″/n ^{k/d+(k−1)/(2d(d−1))}, where c _k,d ,c _k,d ′,c _k,d ″>0 are constants. A preliminary version of this paper appeared in COCOON ’05.