Effectively Closed Infinite-Genus Surfaces and the String Coupling

The class of effectively closed infinite-genus surfaces, defining the completion of the domain of string perturbation theory, can be included in the category $O_G$, which is characterized by the vanishing capacity of the ideal boundary. The cardinality of the maximal set of endpoints is shown to be 2^{\mit N}. The product of the coefficient of the genus-g superstring amplitude in four dimensions by $2^g$ in the $g\to \infty$ limit is an exponential function of the genus with a base comparable in magnitude to the unified gauge coupling. The value of the string coupling is consistent with the characteristics of configurations which provide a dominant contribution to a finite vacuum amplitude.Comment: TeX, 33 page

Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The method we employ in the proof can be considered as fundamental to the integrability of ultradiscrete soliton equations.Comment: 14 pages, 10 figures Added citations in v

On absolute continuity of the spectrum of a periodic magnetic Schr\"odinger operator

We consider the Schr\"odinger operator in ${\mathbb R}^n$, $n\geq 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of the operator in question under some conditions which, in particular, are satisfied if $V\in L^{n/2}_{{\mathrm {loc}}}({\mathbb R}^n)$ and $A\in H^q_{{\mathrm {loc}}}({\mathbb R}^n;{\mathbb R}^n)$, $q>(n-1)/2$.Comment: 25 page

Radio-frequency Bloch-transistor electrometer

A quantum-limited electrometer based on charge modulation of the Josephson supercurrent in the Bloch transistor inserted into a superconducting ring is proposed. As this ring is inductive coupled to a high-Q resonance tank circuit, the variations of the charge on the transistor island (input signal) are converted into variations of amplitude and phase of radio-frequency oscillations in the tank. These variations are amplified and then detected. The output noise, the back-action fluctuations and their cross-correlation are computed. It is shown that our device enables measurements of the charge with a sensitivity which is determined by the energy resolution of its amplifier, that can be reduced down to the standard quantum limit of \hbar/2. On the basis of this setup a "back-action-evading" scheme of the charge measurements is proposed.Comment: 5 pages incl. 2 figure

Application of the Large-N_c limit to a Chiral Lagrangian with Resonances

It is shown that the implementation of the Large--$N_c$ approximation helps to get insight into the structure of, in principle, any QCD-like theory. As an example, we will compute the NLO corrections to $L_{10}$ in the chiral limit with a Lagrangian with Resonances.Comment: 9 pages, 1 figure. Talk given at the International School of Subnuclear Physics (Erice 2002). To be published in the Proceeding

NEW DATA ON AGE AND NATURE OF CARBONIZATION WITHIN SOUTHERN FLANK OF THE BAIKAL LEDGE OF THE SIBERIAN CRATON BASEMENT

The Baikal ledge rock formations in the Siberian craton structure are included in the Akitkan mobile belt which is considered as the Late Paleoproterozoic independent island arc system moved up to the ancient basement during the terrains amalgamation 1.91–2.00 Ga ago (Fig. 1) [Rosen, 2003; Gladkochub et al., 2009; Didenko et al., 2013].The Baikal ledge rock formations in the Siberian craton structure are included in the Akitkan mobile belt which is considered as the Late Paleoproterozoic independent island arc system moved up to the ancient basement during the terrains amalgamation 1.91–2.00 Ga ago (Fig. 1) [Rosen, 2003; Gladkochub et al., 2009; Didenko et al., 2013]

Parity nonconservation effects in the photodesintegration of polarized deuterons

P-odd correlations in the deuteron photodesintegration are considered. The $\pi$-meson exchange is not operative in the case of unpolarized deuterons. For polarized deuterons a P-odd correlation due to the $\pi$-meson exchange is about $3 \times 10^{-9}$. Short-distance P-odd contributions exceed essentially than the contribution of the $\pi$-meson exchange.Comment: 12 pages, Latex, 3 figure

Classification of Reductive Monoid Spaces Over an Arbitrary Field

In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify reductive monoid spaces over an arbitrary field.Comment: This is the final versio

On perturbations of Dirac operators with variable magnetic field of constant direction

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Various situations, for example when the magnetic field is constant, periodic or diverging at infinity, are covered. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.Comment: 12 page