Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

We show that the 1-dimensional Schrödinger equation with a quasiperiodic potential which is analytic on its hull admits a Floquet representation for almost every energyE in the upper part of the spectrum. We prove that the upper part of the spectrum is purely absolutely continuous and that, for a generic potential, it is a Cantor set. We also show that for a small potential these results extend to the whole spectrum.     

Die Autokorrelationsfunktion der von einem Opalglas gestreuten Intensität

Ohne Zusammenfassung     

Modulational and filamentational instabilities of intense photon pulses and their dynamics in a photon gas

It is shown that an intense photon pulse interacting nonlinearly with sound waves in a photon gas is subjected to modulational and filamentational instabilities. Starting from a new set of coupled equations governing nonlinear photon-photon interactions, we derive a dispersion relation which depicts the temporal and spatial amplification rates of the modulational and filamentational instabilities. The long term behavior of the modulationally unstable waves renders collapse of a photon beam as well as the formation of cylindrically symmetric photonic solitons. The results can have relevance to the understanding of the nonlinear photonic pulse propagation in astrophysical environments as well as in forthcoming intense laser-matter interaction experiments.     

Dynamics of electron holes in an electron-oxygen-ion plasma

The dynamics of electron holes (EHs) in an electron-oxygen-ion plasma is studied by means of Vlasov simulations. It is found that EHs are attracted by ion density maxima but repelled by ion density minima. Standing EHs repel ions owing to the positive EH potential, creating an ion density cavity which ejects the EH, which propagates away from the cavity with a constant speed. On the other hand, propagating EHs can be trapped at ion density maxima. The results of our simulations will help in understanding the nonlinear dynamics of EHs in space and laboratory plasmas.     

Nonequilibrium volume plasma chemical processing

A review is presented of plasma chemical processes occurring in the volume part of electrical nonequilibrium discharges. The role of energetic electrons as initiators of chemical reactions in a cold background gas is discussed. Different discharge types of (glow, corona, silent, RF, and microwave discharges) are investigated with respect to their suitability for plasma processing. Emphasis is placed on the requirements of initiating and maintaining the discharge and, at the same time, optimizing plasma parameters for the desired chemical process. Using large-scale industrial ozone production as an example, the detailed process of discharge optimization is described. Other applications of volume plasma processing include other plasma chemical syntheses as well as decomposition processes such as flue gas treatment and hazardous waste disposal. The author only deals with plasmas which are not in equilibrium     

Nonlinear theory for a quantum diode in a dense Fermi magnetoplasma

We present a simple analytical nonlinear theory for quantum diodes in a dense Fermi magnetoplasma. By using the steady-state quantum hydrodynamical equations for a dense Fermi magnetoplasma, we derive coupled nonlinear Schr?dinger and Poisson equations. The latter are numerically solved to show the effects of the quantum statistical pressure, the quantum tunneling (or the quantum diffraction), and the external magnetic field strength on the potential and electron density profiles in a quantum diode at nanometer scales. It is found that the quantum statistical pressure introduces a lower bound on the steady electron flow in the quantum diode, while the quantum diffraction effect allows the electron tunneling at low flow speeds. The magnetic field acts as a barrier, and larger potentials are needed to drive currents through the quantum diode.     

Instability and evolution of nonlinearly interacting water waves

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schr?dinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.     

Imidazolium-modification enhances photocatalytic CO2 reduction on ZnSe quantum dots

Colloidal photocatalysts can utilize solar light for the conversion of CO₂ to carbon-based fuels, but controlling the product selectivity for CO₂ reduction remains challenging, in particular in aqueous solution. Here, we present an organic surface modification strategy to tune the product selectivity of colloidal ZnSe quantum dots (QDs) towards photocatalytic CO₂ reduction even in the absence of transition metal co-catalysts. Besides H₂, imidazolium-modified ZnSe QDs evolve up to 2.4 mmol_CO g_ZnSe⁻¹ (TON_QD > 370) after 10 h of visible light irradiation (AM 1.5G, λ > 400 nm) in aqueous ascorbate solution with a CO-selectivity of up to 20%. This represents a four-fold increase in CO-formation yield and 13-fold increase in CO-selectivity compared to non-functionalized ZnSe QDs. The binding of the thiolated imidazolium ligand to the QD surface is characterized quantitatively using ¹H-NMR spectroscopy and isothermal titration calorimetry, revealing that a subset of 12 to 17 ligands interacts strongly with the QDs. Transient absorption spectroscopy reveals an influence of the ligand on the intrinsic charge carrier dynamics through passivating Zn surface sites. Density functional theory calculations indicate that the imidazolium capping ligand plays a key role in stabilizing the surface-bound *CO₂⁻ intermediate, increasing the yield and selectivity toward CO production. Overall, this work unveils a powerful tool of using organic capping ligands to modify the chemical environment on colloids, thus enabling control over the product selectivity within photocatalyzed CO₂ reduction.

A photocatalyst system consisting of ZnSe quantum dots modified with a thiolated imidazolium capping ligand for visible light-driven reduction of aqueous CO₂ to CO is reported without the need for a metal complex co-catalyst.