A quantum group version of quantum gauge theories in two dimensions

For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is based on ideas of Migdal. The main ingredient is the Turaev-Viro combinatorial construction of topological invariants of closed, compact 3-manifolds and its extension to arbitrary compact 3-manifolds as given by the authors in collaboration with W. Mueller.Comment: 6 pages (plain TeX

An alternative to the conventional micro-canonical ensemble

Usual approach to the foundations of quantum statistical physics is based on conventional micro-canonical ensemble as a starting point for deriving Boltzmann-Gibbs (BG) equilibrium. It leaves, however, a number of conceptual and practical questions unanswered. Here we discuss these questions, thereby motivating the study of a natural alternative known as Quantum Micro-Canonical (QMC) ensemble. We present a detailed numerical study of the properties of the QMC ensemble for finite quantum systems revealing a good agreement with the existing analytical results for large quantum systems. We also propose the way to introduce analytical corrections accounting for finite-size effects. With the above corrections, the agreement between the analytical and the numerical results becomes very accurate. The QMC ensemble leads to an unconventional kind of equilibrium, which may be realizable after strong perturbations in small isolated quantum systems having large number of levels. We demonstrate that the variance of energy fluctuations can be used to discriminate the QMC equilibrium from the BG equilibrium. We further suggest that the reason, why BG equilibrium commonly occurs in nature rather than the QMC-type equilibrium, has something to do with the notion of quantum collapse.Comment: 25 pages, 6 figure

A Study of Oxidation of Hydrogen Based on Flashback of Hydrogen-Oxygen-Nitrogen Burner Flames

The flashback of hydrogen-oxygen-nitrogen flames was studied as a function of pressure, burner diameter, equivalence ratio, and oxidant strength. The results were treated on the assumption that the product of the critical boundary velocity gradient for flashback and the initial concentration of that reactant which is not in excess is proportional to a mean reaction rate associated with the flame zone. It was further assumed that this reaction rate can be expressed in terms of initial concentrations and flame temperature. Measurements at constant flame temperature yield orders of reaction with respect to hydrogen and oxygen. These do not vary with flame temperature. Measurements in which pressure is varied for several values of oxidant strength at constant equivalence ratio yield a total order of reaction and a function describing the dependence of the mean reaction rate on flame temperature. The total reaction order is independent of flame temperature and equal to the sum of the orders for hydrogen and oxygen. The dependence of the reaction rate on flame temperature cannot be described by a constant activation energy. The activation energy obtained apparently increases with flame temperature. Flashback results can be described by a single rate constant which is independent of equivalence ratio. Values were estimated for this rate constant as a function of flame temperature

A model of ganglion axon pathways accounts for percepts elicited by retinal implants.

Degenerative retinal diseases such as retinitis pigmentosa and macular degeneration cause irreversible vision loss in more than 10 million people worldwide. Retinal prostheses, now implanted in over 250 patients worldwide, electrically stimulate surviving cells in order to evoke neuronal responses that are interpreted by the brain as visual percepts ('phosphenes'). However, instead of seeing focal spots of light, current implant users perceive highly distorted phosphenes that vary in shape both across subjects and electrodes. We characterized these distortions by asking users of the Argus retinal prosthesis system (Second Sight Medical Products Inc.) to draw electrically elicited percepts on a touchscreen. Using ophthalmic fundus imaging and computational modeling, we show that elicited percepts can be accurately predicted by the topographic organization of optic nerve fiber bundles in each subject's retina, successfully replicating visual percepts ranging from 'blobs' to oriented 'streaks' and 'wedges' depending on the retinal location of the stimulating electrode. This provides the first evidence that activation of passing axon fibers accounts for the rich repertoire of phosphene shape commonly reported in psychophysical experiments, which can severely distort the quality of the generated visual experience. Overall our findings argue for more detailed modeling of biological detail across neural engineering applications