A differential method for bounding the ground state energy

For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a normalisation factor or a matrix element). It just requires the determination of the absolute minimum and maximum in the whole configuration space of the local energy associated with a normalisable trial function (the calculation of the norm is not needed). After a general introduction, the method is applied to three non-integrable systems: the asymmetric annular billiard, the many-body spinless Coulombian problem, the hydrogen atom in a constant and uniform magnetic field. Being more sensitive than the variational methods to any local perturbation of the trial function, this method can used to systematically improve the energy bounds with a local skilled analysis; an algorithm relying on this method can therefore be constructed and an explicit example for a one-dimensional problem is given.Comment: Accepted for publication in Journal of Physics

Mechanism of Deep-focus Earthquakes Anomalous Statistics

Analyzing the NEIC-data we have shown that the spatial deep-focus earthquake distribution in the Earth interior over the 1993-2006 is characterized by the clearly defined periodical fine discrete structure with period L=50 km, which is solely generated by earthquakes with magnitude M 3.9 to 5.3 and only on the convergent boundary of plates. To describe the formation of this structure we used the model of complex systems by A. Volynskii and S. Bazhenov. The key property of this model consists in the presence of a rigid coating on a soft substratum. It is shown that in subduction processes the role of a rigid coating plays the slab substance (lithosphere) and the upper mantle acts as a soft substratum. Within the framework of this model we have obtained the estimation of average values of stress in the upper mantle and Young's modulus for the oceanic slab (lithosphere) and upper mantle.Comment: 9 pages, 7 figure

Fuzzy Geometry of Phase Space and Quantization of Massive Fields

The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy point. Due to Foset partial (weak) ordering, particle's space coordinate x acquires principal uncertainty dx. It's shown that Shroedinger formalism of Quantum Mechanics can be completely derived from consideration of particle evolution in fuzzy phase space with minimal number of axioms.Comment: 13 pages, Talk given at QFEXT07 Workshop, Leipzig, Sept. 200

Aspects of hairy black holes in spontaneously-broken Einstein-Yang-Mills systems: Stability analysis and Entropy considerations

We analyze (3+1)-dimensional black-hole space-times in spontaneously broken Yang-Mills gauge theories that have been recently presented as candidates for an evasion of the scalar-no-hair theorem. Although we show that in principle the conditions for the no-hair theorem do not apply to this case, however we prove that the `spirit' of the theorem is not violated, in the sense that there exist instabilities, in both the sphaleron and gravitational sectors. The instability analysis of the sphaleron sector, which was expected to be unstable for topological reasons, is performed by means of a variational method. As shown, there exist modes in this sector that are unstable against linear perturbations. Instabilities exist also in the gravitational sector. A method for counting the gravitational unstable modes, which utilizes a catastrophe-theoretic approach is presented. The r\^ole of the catastrophe functional is played by the mass functional of the black hole. The Higgs vacuum expectation value (v.e.v.) is used as a control parameter, having a critical value beyond which instabilities are turned on. The (stable) Schwarzschild solution is then understood from this point of view. The catastrophe-theory appproach facilitates enormously a universal stability study of non-Abelian black holes, which goes beyond linearized perturbations. Some elementary entropy considerations are also presented...Comment: Latex file, 50 pages, 2 figures (included as PS files at the end: plot1.ps, plot2.ps

Analysis of a three-component model phase diagram by Catastrophe Theory

We analyze the thermodynamical potential of a lattice gas model with three components and five parameters using the methods of Catastrophe Theory. We find the highest singularity, which has codimension five, and establish its transversality. Hence the corresponding seven-degree Landau potential, the canonical form Wigwam or $A_6$, constitutes the adequate starting point to study the overall phase diagram of this model.Comment: 16 pages, Latex file, submitted to Phys. Rev.

Hepatic rhythmicity of endoplasmic reticulum stress is disrupted in perinatal and adult mice models of high-fat diet-induced obesity

We investigated the regulation of hepatic ER stress in healthy liver and adult or perinatally programmed diet-induced non-alcoholic fatty liver disease (NAFLD). Female mice were fed either obesogenic or control diet before mating, during pregnancy and lactation. Post-weaning, offspring from each maternal group were divided into either obesogenic or control diet. At six months, offspring were sacrificed at 4-h intervals over 24 h. Offspring fed obesogenic diets developed NAFLD phenotype, and the combination of maternal and offspring obesogenic diets exacerbated this phenotype. UPR signalling pathways (IREα, PERK, ATF6) and their downstream regulators showed different basal rhythmicity, which was modified in offspring exposed to obesogenic diet and maternal programming. The double obesogenic hit increased liver apoptosis measured by TUNEL staining, active caspase-3 and phospho-JNK and GRP78 promoter methylation levels. This study demonstrates that hepatic UPR is rhythmically activated. The combination of maternal obesity (MO) and obesogenic diets in offspring triggered altered UPR rhythmicity, DNA methylation and cellular apoptosis

Visible Near-infrared Spectral Evolution of Irradiated Mixed Ices and Application to Kuiper Belt Objects and Jupiter Trojans

Understanding the history of Kuiper Belt Objects and Jupiter Trojans will help to constrain models of solar system formation and dynamical evolution. Laboratory simulations of a possible thermal and irradiation history of these bodies were conducted on ice mixtures while monitoring their spectral properties. These simulations tested the hypothesis that the presence or absence of sulfur explains the two distinct visible near-infrared spectral groups observed in each population and that Trojans and KBOs share a common formation location. Mixed ices consisting of water, methanol, and ammonia, in mixtures both with and without hydrogen sulfide, were deposited and irradiated with 10 keV electrons. Deposition and initial irradiation were performed at 50 K to simulate formation at 20 au in the early solar system, then heated to Trojan-like temperatures and irradiated further. Finally, irradiation was concluded and resulting samples were observed during heating to room temperature. Results indicated that the presence of sulfur resulted in steeper spectral slopes. Heating through the 140–200 K range decreased the slopes and total reflectance for both mixtures. In addition, absorption features at 410, 620, and 900 nm appeared under irradiation, but only in the H_2S-containing mixture. These features were lost with heating once irradiation was concluded. While the results reported here are consistent with the hypothesis, additional work is needed to address uncertainties and to simulate conditions not included in the present work

Propagation of charged particle waves in a uniform magnetic field

This paper considers the probability density and current distributions generated by a point-like, isotropic source of monoenergetic charges embedded into a uniform magnetic field environment. Electron sources of this kind have been realized in recent photodetachment microscopy experiments. Unlike the total photocurrent cross section, which is largely understood, the spatial profiles of charge and current emitted by the source display an unexpected hierarchy of complex patterns, even though the distributions, apart from scaling, depend only on a single physical parameter. We examine the electron dynamics both by solving the quantum problem, i. e., finding the energy Green function, and from a semiclassical perspective based on the simple cyclotron orbits followed by the electron. Simulations suggest that the semiclassical method, which involves here interference between an infinite set of paths, faithfully reproduces the features observed in the quantum solution, even in extreme circumstances, and lends itself to an interpretation of some (though not all) of the rich structure exhibited in this simple problem.Comment: 39 pages, 16 figure

Electron Irradiation and Thermal Processing of Mixed-ices of Potential Relevance to Jupiter Trojan Asteroids

In this work we explore the chemistry that occurs during the irradiation of ice mixtures on planetary surfaces, with the goal of linking the presence of specific chemical compounds to their formation locations in the solar system and subsequent processing by later migration inward. We focus on the outer solar system and the chemical differences for ice mixtures inside and outside the stability line for H_2S. We perform a set of experiments to explore the hypothesis advanced by Wong & Brown that links the color bimodality in Jupiter's Trojans to the presence of H_2S in the surface of their precursors. Non-thermal (10 keV electron irradiation) and thermally driven chemistry of CH_3OH–NH_3–H_2O ("without H_2S") and H_2S–CH_3OH–NH_3–H_2O ("with H_2S") ices were examined. Mid-IR analyses of ice and mass spectrometry monitoring of the volatiles released during heating show a rich chemistry in both of the ice mixtures. The "with H_2S" mixture experiment shows a rapid consumption of H_2S molecules and production of OCS molecules after a few hours of irradiation. The heating of the irradiated "with H_2S" mixture to temperatures above 120 K leads to the appearance of new infrared bands that we provisionally assign to SO_2 and CS. We show that radiolysis products are stable under the temperature and irradiation conditions of Jupiter Trojan asteroids. This makes them suitable target molecules for potential future missions as well as telescope observations with a high signal-to-noise ratio. We also suggest the consideration of sulfur chemistry in the theoretical modeling aimed at understanding the chemical composition of Trojans and KOBs