Transport in dimerized and frustrated spin systems

We analyze the Drude weight for both spin and thermal transport of one-dimensional spin-1/2 systems by means of exact diagonalization at finite temperatures. While the Drude weights are non-zero for finite systems, we find indications of a vanishing of the Drude weights in the thermodynamic limit for non-integrable models implying normal transport behavior.Comment: 2 pages, 1 figure. Proceedings of the ICM 2003, Rom

Molecular analysis of the distribution and phylogeny of the soxB gene among sulfur-oxidizing bacteria - evolution of the Sox sulfur-oxidizing enzyme system

The soxB gene encodes the SoxB component of the periplasmic thiosulfate-oxidizing Sox enzyme complex, which has been proposed to be widespread among the various phylogenetic groups of sulfur-oxidizing bacteria (SOB) that convert thiosulfate to sulfate with and without the formation of sulfur globules as intermediate. Indeed, the comprehensive genetic and genomic analyses presented in the present study identified the soxB gene in 121 phylogenetically and physiologically divergent SOB, including several species for which thiosulfate utilization has not been reported yet. In first support of the previously postulated general involvement of components of the Sox enzyme complex in the thiosulfate oxidation process of sulfur-storing SOB, the soxB gene was detected in all investigated photo- and chemotrophic species that form sulfur globules during thiosulfate oxidation (Chromatiaceae, Chlorobiaceae, Ectothiorhodospiraceae, Thiothrix, Beggiatoa, Thiobacillus, invertebrate symbionts and free-living relatives). The SoxB phylogeny reflected the major 16S rRNA gene-based phylogenetic lineages of the investigated SOB, although topological discrepancies indicated several events of lateral soxB gene transfer among the SOB, e.g. its independent acquisition by the anaerobic anoxygenic phototrophic lineages from different chemotrophic donor lineages. A putative scenario for the proteobacterial origin and evolution of the Sox enzyme system in SOB is presented considering the phylogenetic, genomic (sox gene cluster composition) and geochemical data

Thermal Conductivity of Spin-1/2 Chains

We study the low-temperature transport properties of clean one-dimensional spin-1/2 chains coupled to phonons. Due to the presence of approximate conservation laws, the heat current decays very slowly giving rise to an exponentially large heat conductivity, $\kappa ~ e^{T^*/T}$. As a result of an interplay of Umklapp scattering and spinon-phonon coupling, the characteristic energy scale $T^*$ turns out to be of order $\Theta_D/2$, where $\Theta_D$ is the Debye energy, rather than the magnetic exchange interaction $J$ -- in agreement with recent measurements in SrCuO compounds. A large magnetic field strongly affects the heat transport by two distinct mechanisms. First, it induces a LINEAR spinon--phonon coupling, which alters the nature of the $T -> 0$ fixed point: the elementary excitations of the system are COMPOSITE SPINON-PHONON objects. Second, the change of the magnetization and the corresponding change of the wave vector of the spinons strongly affects the way in which various Umklapp processes can relax the heat current, leading to a characteristic fractal--like spiky behavior of $\kappa$ when plotted as a function of magnetization at fixed T.Comment: 16 pages, RevTex4, 2 figures included; revised refs. and some useful comments on experimental relevance. On July 12 2005, added an appendix correcting an error in the form of the phonon propagator. The main result is unchange

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev

Field Theoretical Quantum Effects on the Kerr Geometry

We study quantum aspects of the Einstein gravity with one time-like and one space-like Killing vector commuting with each other. The theory is formulated as a \coset nonlinear $\sigma$-model coupled to gravity. The quantum analysis of the nonlinear $\sigma$-model part, which includes all the dynamical degrees of freedom, can be carried out in a parallel way to ordinary nonlinear $\sigma$-models in spite of the existence of an unusual coupling. This means that we can investigate consistently the quantum properties of the Einstein gravity, though we are limited to the fluctuations depending only on two coordinates. We find the forms of the beta functions to all orders up to numerical coefficients. Finally we consider the quantum effects of the renormalization on the Kerr black hole as an example. It turns out that the asymptotically flat region remains intact and stable, while, in a certain approximation, it is shown that the inner geometry changes considerably however small the quantum effects may be.Comment: 16 pages, LaTeX. The hep-th number added on the cover, and minor typos correcte

Study of the p p -> p p pi+ pi- Reaction in the Low-Energy Tail of the Roper Resonance

Exclusive measurements of the p p -> p p pi+ pi- reaction have been carried out at Tp = 775 MeV at CELSIUS using the PROMICE/WASA setup. Together with data obtained at lower energy they point to a dominance of the Roper excitation in this process. From the observed interference of its decay routes N* -> N sigma and N* -> Delta pi -> N sigma their energy-dependent relative branching ratio is determined

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a channel is developed. This is based on the global study of the phase space structure of the low-dimensional ODE's defined by the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail, and general proofs concerning properties of fixed points and existence of finite-time singularities for broad classes of solutions are given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. The main conclusion is that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space spanning a sufficiently large set of initial conditions, are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding of them does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is discussed as the key point for a generic Dynamical Solvability Scenario which is proposed for a general context of interfacial pattern selection.Comment: 3 figures added, major rewriting of some sections, submitted to Phys. Rev.

Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste