Ergodicity criteria for non-expanding transformations of 2-adic spheres

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems $$ on 2-adic spheres $\mathbf S_{2^{-r}}(a)$ of radius $2^{-r}$, $r\ge 1$, centered at some point $a$ from the ultrametric space of 2-adic integers $\mathbb Z_2$. The map $f\colon\mathbb Z_2\to\mathbb Z_2$ is assumed to be non-expanding and measure-preserving; that is, $f$ satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and $f$ preserves a natural probability measure on $\mathbb Z_2$, the Haar measure $\mu_2$ on $\mathbb Z_2$ which is normalized so that $\mu_2(\mathbb Z_2)=1$

The Non-Archimedean Theory of Discrete Systems

In the paper, we study behavior of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behavior of the system w.r.t. variety of word transformations performed by the system: We call a system completely transitive if, given arbitrary pair $a,b$ of finite words that have equal lengths, the system $\mathfrak A$, while evolution during (discrete) time, at a certain moment transforms $a$ into $b$. To every system $\mathfrak A$, we put into a correspondence a family $\mathcal F_{\mathfrak A}$ of continuous maps of a suitable non-Archimedean metric space and show that the system is completely transitive if and only if the family $\mathcal F_{\mathfrak A}$ is ergodic w.r.t. the Haar measure; then we find easy-to-verify conditions the system must satisfy to be completely transitive. The theory can be applied to analyze behavior of straight-line computer programs (in particular, pseudo-random number generators that are used in cryptography and simulations) since basic CPU instructions (both numerical and logical) can be considered as continuous maps of a (non-Archimedean) metric space $\mathbb Z_2$ of 2-adic integers.Comment: The extended version of the talk given at MACIS-201

Production of (τ+τ−)b(\tau^+\tau^-)_b in electron positron collisions

$(\tau^+\tau^-)_b$ is an atom of simple hydrogenlike structure similar to positronium $(e^+e^-)_b$ and $(\mu^+\mu^-)_b$. In this paper energy levels and decay widths of different decay channels of $(\tau^+\tau^-)_b$ are given. Cross section of production of this atomic system in $e^+e^-$ annihilation taking into account radiative corrections is calculated. According to our estimates 886 $(\tau^+\tau^-)_b$ atoms may be produced at BEPCII and 29 $(\tau^+\tau^-)_b$ atoms are produced at VEPP-4M under the present experimental conditions.Comment: 5 pages, submitted to Int. Jour. Mod. Phys.

Photon Stimulated Desorption and the Effect of Cracking of Condensed Molecules in a Cryogenic Vacuum System

The design of the Large Hadron Collider (LHC) vacuum system requires a complete understanding of all processes which may affect the residual gas density in the cold bore of the 1.9 K cryomagnets. A wealth of data has been obtained which may be used to predict the residual gas density inside a cold vacuum system exposed to synchrotron radiation. In this study the effect of cracking of cryosorbed molecules by synchrotron radiation photons has been included. Cracking of the molecular species CO2 and CH4 has been observed in recent studies and these findings have been incorporated in a more detailed dynamic gas density model for the LHC. In this paper, we describe the relevant physical processes and the parameters required for a full evaluation. It is shown that the dominant gas species in the LHC vacuum system with its beam screen are H2 and CO. The important result of this study is that while the surface coverage of cryosorbed CH4 and CO2 molecules is limited due to cracking, the coverage of H2 and CO molecules may increase steadily during the long term operation of the machine

T-functions revisited: New criteria for bijectivity/transitivity

The paper presents new criteria for bijectivity/transitivity of T-functions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz $p$-adic functions and to study measure-preservation/ergodicity of these

A hydrogen ion beam method of molecular density measurement inside a 4.2-K beam tube

In our first experiments on synchrotron radiation-induced photodesorption in a 4.2-K beam tube, the moleculm density was measured by room temperature ion gauges and RGAs outside the beam tube. The molecular density inside the 4.2-K beam tube was therefore unknown, since the mean molecular speed of photodesorbed molecules had not been measured. To determine the density inside the 4.2-K beam tube we have developed a direct method of measurement utilizing the neutralization of H{sup +} beams, which are proportional to gas density. The hydrogen ion beams (up to 20 keV, {approximately}1 {mu}A) are extracted from an rf ion source and guided into the cold beam tube by a bending magnet. The H{sup 0} and H{sup {minus}} produced in the beam tube are magnetically separated from H{sup {minus}} and detected with secondary electron multipliers (SEMs). Small superconducting dipole magnets located near the center of the beam tube allow a {approximately}20-cm segment of the injected ion beam to be offset a few mm from the injection axis; detection of H{sup 0} and H{sup {minus}} produced along this offset segment provides a localized density measurement. If necessary, detector background due to synchrotron radiation photons can be discriminated against by gating the detector on between the bursts of synchrotron radiation. The experimental setup and initial data will be presented

Reflection of photons and azimuthal distribution of photoelectrons in a cylindrical beam pipe

In a cryogenic proton accelerator, such as the LHC, the creation of an electron cloud and generated heat loads resulting from electron bombardment are strongly dependent on the azimuthal distribution of created photoelectrons. In this context, photon reflection and photoelectron yield measurements have been performed using a beam line on the VEPP-2M storage ring. Six electrodes, covering the complete vacuum chamber perimeter, were mounted such that they could be suitably biased, and while one electrode was irradiated with synchrotron radiation the resulting electron current of all others could be measured. A detailed description of the experimental apparatus and the results of the measurements of photon reflection and the azimuthal distribution of generated photoelectrons are presented