Modular Invariance and Uniqueness of Conformal Characters

We show that the conformal characters of various rational models of W-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result we develop several tools for studying representations of SL(2,Z) on spaces of modular functions. These methods, applied here only to certain rational conformal field theories, may be useful for the analysis of many others.Comment: 21 pages (AMS TeX), BONN-TH-94-16, MPI-94-6

Atomistic simulations of self-trapped exciton formation in silicon nanostructures: The transition from quantum dots to nanowires

Using an approximate time-dependent density functional theory method, we calculate the absorption and luminescence spectra for hydrogen passivated silicon nanoscale structures with large aspect ratio. The effect of electron confinement in axial and radial directions is systematically investigated. Excited state relaxation leads to significant Stokes shifts for short nanorods with lengths less than 2 nm, but has little effect on the luminescence intensity. The formation of self-trapped excitons is likewise observed for short nanostructures only; longer wires exhibit fully delocalized excitons with neglible geometrical distortion at the excited state minimum.Comment: 10 pages, 4 figure

Molecular dynamics simulation studies of the interactions between ionic liquids and amino acids in aqueous solution

Although the understanding of the influence of ionic liquids (ILs) on the solubility behavior of biomolecules in aqueous solutions is relevant for the design and optimization of novel biotechnological processes, the underlying molecular-level mechanisms are not yet consensual or clearly elucidated. In order to contribute to the understanding of the molecular interactions established between amino acids and ILs in aqueous media, classical molecular dynamics (MD) simulations were performed for aqueous solutions of five amino acids with different structural characteristics (glycine, alanine, valine, isoleucine, and glutamic acid) in the presence of 1-butyl-3-methylimidazolium bis(trifluoromethyl)sulfonyl imide. The results from MD simulations enable to relate the properties of the amino acids, namely their hydrophobicity, to the type and strength of their interactions with ILs in aqueous solutions and provide an explanation for the direction and magnitude of the solubility phenomena observed in [IL + amino acid + water] systems by a mechanism governed by a balance between competitive interactions of the IL cation, IL anion, and water with the amino acids