Polarizations and Nullcone of Representations of Reductive Groups

The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of $SL_2$ on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.

Vacancy diffusion in the triangular lattice dimer model

We study vacancy diffusion on the classical triangular lattice dimer model, sub ject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e. a monomer, in an otherwise fully packed lattice, is always localized in a tree-like structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16 \pm 0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous:Comment: 15 pages, 27 eps figures. submitted to Physical Review

Two-band ferromagnetic Kondo-lattice model for local-moment half-metals

We introduce a two-band Kondo-lattice model to describe ferromagnetic half-metals with local magnetic moments. In a model study, the electronic and magnetic properties are presented by temperature dependent magnetization curves, band-structures, spin polarizations and plasma frequencies. These are obtained from numerically evaluated equations, based on the single-electron Green functions. We show that the mutual influence between the itinerant electrons and the local magnetic moments is responsible for several phase transitions of the half-metals, namely first and second order magnetic phase transitions, as well as half-metal to semiconductor and half-metal to semimetal transitions.Comment: 10 pages, 5 figures, submitted to Journal of Physics: Condensed Matte

A confirmed location in the Galactic halo for the high-velocity cloud 'chain A'

The high-velocity clouds of atomic hydrogen, discovered about 35 years ago, have velocities inconsistent with simple Galactic rotation models that generally fit the stars and gas in the Milky Way disk. Their origins and role in Galactic evolution remain poorly understood, largely for lack of information on their distances. The high-velocity clouds might result from gas blown from the Milky Way disk into the halo by supernovae, in which case they would enrich the Galaxy with heavy elements as they fall back onto the disk. Alternatively, they may consist of metal-poor gas -- remnants of the era of galaxy formation, accreted by the Galaxy and reducing its metal abundance. Or they might be truly extragalactic objects in the Local Group of galaxies. Here we report a firm distance bracket for a large high-velocity cloud, Chain A, which places it in the Milky Way halo (2.5 to 7 kiloparsecs above the Galactic plane), rather than at an extragalactic distance, and constrains its gas mass to between 10^5 and 2 times 10^6 solar masses.Comment: 8 pages, including 4 postscript figures. Letter to Nature, 8 July 199

On Duality in the Born-Infeld Theory

The $SL(2,R)$ duality symmetric action for the Born-Infeld theory in terms of two potentials, coupled with non-trivial backgroud fields in four dimensions is established. This construction is carried out in detail by analysing the hamiltonian structure of the Born-Infeld theory. The equivalence with the usual Born-Infeld theory is shown.Comment: revtex, 4 page

Reconnection and acoustic emission of quantized vortices in superfluid by the numerical analysis of the Gross-Pitaevskii equation

We study numerically the reconnection of quantized vortices and the concurrent acoustic emission by the analysis of the Gross-Pitaevskii equation. Two quantized vortices reconnect following the process similar to classical vortices; they approach, twist themselves locally so that they become anti-parallel at the closest place, reconnect and leave separately.The investigation of the motion of the singular lines where the amplitude of the wave function vanishes in the vortex cores confirms that they follow the above scenario by reconnecting at a point. This reconnection is not contradictory to the Kelvin's circulation theorem, because the potential of the superflow field becomes undefined at the reconnection point. When the locally anti-parallel part of the vortices becomes closer than the healing length, it moves with the velocity comparable to the sound velocity, emits the sound waves and leads to the pair annihilation or reconnection; this phenomena is concerned with the Cherenkov resonance. The vortices are broken up to smaller vortex loops through a series of reconnection, eventually disappearing with the acoustic emission. This may correspond to the final stage of the vortex cascade process proposed by Feynman. The change in energy components, such as the quantum, the compressible and incompressible kinetic energy is analyzed for each dynamics. The propagation of the sound waves not only appears in the profile of the amplitude of the wave function but also affects the field of its phase, transforming the quantum energy due to the vortex cores to the kinetic energy of the phase field.Comment: 11 pages, 16 figures, LaTe

S-Duality at the Black Hole Threshold in Gravitational Collapse

We study gravitational collapse of the axion/dilaton field in classical low energy string theory, at the threshold for black hole formation. A new critical solution is derived that is spherically symmetric and continuously self-similar. The universal scaling and echoing behavior discovered by Choptuik in gravitational collapse appear in a somewhat different form. In particular, echoing takes the form of SL(2,R) rotations (cf. S-duality). The collapse leaves behind an outgoing pulse of axion/dilaton radiation, with nearly but not exactly flat spacetime within it.Comment: 8 pages of LaTeX, uses style "revtex"; 1 figure, available in archive, or at ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-15.ep

Vagus Nerve Stimulation in Refractory Epilepsy: Effects on Pro- and Anti-Inflammatory Cytokines in Peripheral Blood

Objective: The vagus nerve has important immunological functions that may be relevant for its anticonvulsive action. We postulate that this anticonvulsive action is activated by a shift in the immune system resulting in a reduction of neurotoxic and an increase of neuroprotective tryptophan metabolites. Methods: Eleven patients with refractory epilepsy and 11 controls matched for age and gender were included in this study. The primary outcome measure was a 50% seizure reduction. Other variables were pro-inflammatory cytokines IL-6 and TNF-alpha, anti-inflammatory cytokine IL-10, cortisol, and the tryptophan metabolites 3-hydroxykynurenine (3-OH-KYN), kynurenic acid (KYNA), kynurenine, serotonin (5-HT) and 5-hydroxyindol acetic acid (5-HIAA). Blood samples were scheduled during baseline, and in week 28 of add-on treatment. Results: IL-6 levels were higher in the responders than in the control group, and decreased after vagus nerve stimulation (VNS), whereas IL-10 was low and increased after VNS. In nonresponders, VNS resulted in an increase of IL-6 plasma levels and in a decrease of IL-10. Cortisol concentrations are higher in the epilepsy group than in the control group. After VNS, these concentrations decreased. The concentrations of the tryptophan metabolites were lower in the epilepsy group than in the control group. The KYNA ratios are defined as the ratio of neuroprotective KYNA versus neurotoxic 3-OH-KYN and KYNA versus neurotoxic kynurenine: these ratios were lower in epilepsy patients than in controls, and they both moderately increased after VNS. Conclusion: The outcome of this preliminary study indicates that VNS causes a rebalancing of the immune system. This results in: (1) a reduction of neurotoxic and an increase of neuroprotective kynurenine metabolites and (2) in the normalization of cortisol levels. Copyright (C) 2010 S. Karger AG, Base