Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials

 Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site W _r (𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe ³ /q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for W _r (𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice. Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003 RID="*" ID="*" Partially supported by CNPq (Brazil) RID="**" ID="**" Partially supported by CNR, G.N.F.M. (Italy) Communicated by H. Spohn     

Measurement of high-Q e<Superscript>-</Superscript>p neutral current cross sections at HERA and the extraction of xF<Subscript>3</Subscript>

Cross sections for e^-p neutral current deep inelastic scattering have been measured at a centre-of-mass energy of 318 GeV using an integrated luminosity of 15.9 pb^-1 collected with the ZEUS detector at HERA. Results on the double-differential cross-section in the range 185 &lt; Q ² &lt; 50 000 GeV² and 0.0037 &lt; x &lt; 0.75, as well as the single-differential cross-sections , and for Q ² &gt; 200 GeV², are presented. To study the effect of Z-boson exchange, has also been measured for Q ² &gt; 10 000 GeV². The structure function xF₃ has been extracted by combining the e^-p results presented here with the recent ZEUS measurements of e⁺p neutral current deep inelastic scattering. All results agree well with the predictions of the Standard Model. Received: 2 August 2002 / Revised version: 30 January 2003 / Published online: 24 March 2003     

An introduction to physical theory of molecular evolution

This work is a tutorial in Molecular Evolution from the point of view of Physics. We discuss Eigen's model, a link between evolutionary theory and physics. We will begin by assuming the existence of (marco) molecules or replicators with the template property, that is, the capacity to self-replicate. According to this assumption, information will be randomly generated and destroyed by mutations in the code (i.e., errors in the copying process) and new bits of information will be fixed (made stable) by the existence of an external pressure on the system (i.e., selection), and the ability of the molecules to replicate themselves. Our aim is to build a model in order to describe molecular evolution from as general a standpoint as possible. As we will see, even very simple models from the theoretical point of view will have surprisingly deep consequences.     

Enhanced Binding in Non-Relativistic QED

 We consider a spinless particle coupled to a photon field and prove that even if the Schr?dinger operator p ² +V does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant α is small. Received: 7 January 2002 / Accepted: 8 November 2002 Published online: 13 January 2003     

Planting in his Neighbor's Garden: David Hilbert and Early Göttingen Quantum Physics

David Hilbert (1862-1943) played an important role in establishing quantum physics in Göttingen. I analyze the ways in which his influence was decisive by comparison with Woldemar Voigt (1850-1919). Voigt was the leading Göttingen theoretical physicist before the arrival of Peter Debye (1884-1966), who was appointed to a new professorship in 1914 at Hilbert's instigation. I portray the Göttingen mathematicians, above all Hermann Minkowski (1864-1909) and David Hilbert, as planting the seeds for the blossoming of quantum physics under their student Max Born (1882-1970) in the 1920s.     

Energy and momentum losses in the process of neutrino scattering on plasma electrons in the presence of a magnetic field

The neutrino-electron scattering in a dense degenerate magnetized plasma under the conditions μ ² > 2eB ≫ μE is investigated. The volume density of the neutrino energy and momentum losses due to this process are calculated. The results we have obtained demonstrate that plasma in the presence of an external magnetic field is more transparent for neutrino than for non-magnetized plasma. It is shown that neutrino scattering under conditions considered does not lead to the neutrino force acting on plasma.     

Light Scattering Changes in Isolated Brain Mitochondria during Anoxia - Magnesium Effect on Morphological Changes and Respiration -

Under pathological conditions, morphological changes of the cells and tissues may differ from those of normal conditions, which can be reflected by changes in light scattering (LS). Consequently, LS has been recognized as a potential non-invasive tool for optical diagnosis of living tissue. This paper aimed to identify the basic properties of LS of isolated brain mitochondria in vitro under normoxic and anoxic conditions in the presence and absence of Mg²⁺. An increase in LS was observed during anoxia in both the presence and absence of Mg²⁺. In both cases, the changes in LS initiated by anoxia and reoxygenation started concomitantly with the reduction of heme aa₃. The rates of LS changes were slower than those of heme aa₃, particularly in the presence of Mg²⁺. Mg²⁺ inhibited the morphological responses of mitochondria caused by the addition of ADP and ATP, and significantly reduced the oxygen consumption rate in state 4. These results are due to modulation of the K⁺/H⁺ antiporter affected by Mg²⁺. In addition, the mitochondria were well coupled, although the basal level of LS fell after addition of Mg²⁺. Therefore, the observed responses of mitochondria at anoxia were physiological and independent of the presence or absence of Mg²⁺. The relationship between LS and redox state of cytochrome c oxidase, an anoxic indicator, provides a basis to assess the tissue conditions in vivo.     

Applying a Mode Selector to Improve the Pulse-Compression Performance of Asymmetric-Coupled-Waveguide-Based Dispersion Compensators

An InGaAsP slab-type asymmetric-coupled-waveguide-based dispersion compensator with a mode selector has been designed and fabricated. The mode selector is necessary to select either a symmetric [with a positive group-velocity dispersion (GVD)] or antisymmetric (with a negative GVD) supermode. These supermodes exist simultaneously in the dispersion-compensation region of the device. Pulse-compression experiments were used to test the dispersion compensator, evaluating the function of the mode selector. A theoretical study of the experimental results shows that the mode selector obtains a very strong selectivity (nearly 100%) for the antisymmetric supermode.     

Application of the Volterra filter in experimental diffraction data processing

The effective signal in x-ray diffraction analysis of material properties often contains high frequency (noise) and low frequency (trend) components as additive parts. It is necessary to extract the effective signal from the noise to ensure high quality of signal processing. Digital filters of Volterra type are proposed for filtering purposes and a comparison of Volterra filtration implemented on x-ray diffraction data versus results from a set of other digital filters is given.