Harmonic oscillators in the Nos\'e - Hoover thermostat

We study the dynamics of an ensemble of non-interacting harmonic oscillators in a nonlinear dissipative environment described by the Nos\'e - Hoover model. Using numerical simulation we find the histogram for total energy, which agrees with the analysis of the Nos\'e - Hoover equations effected with the method of averaging. The histogram does not correspond to Gibbs' canonical distribution. We have found oscillations at frequency proportional to $\sqrt{\alpha/m}$, $\alpha$ the dissipative parameter of thermostat and $m$ the characteristic mass of particle, about the stationary state corresponding to equilibrium. The oscillations could have an important bearing upon the analysis of simulating molecular dynamics in the Nos\'e - Hoover thermostat.Comment: 7 pages, 4 figure

2d Gauge Theories and Generalized Geometry

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$ by means of composite fields. Gauge transformations of the composite fields follow the Courant bracket, closing upon the choice of a Dirac structure $D \subset \mathbb{T}M$ (or, more generally, the choide of a "small Dirac-Rinehart sheaf" $\cal{D}$), in which the fields as well as the symmetry parameters are to take values. In these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma model, which is applicable in a more general context and proves to be universal in two space-time dimensions: A gauging of $\mathfrak{g}$ of a standard sigma model with Wess-Zumino term exists, \emph{iff} there is a prolongation of the rigid symmetry to a Lie algebroid morphism from the action Lie algebroid $M \times \mathfrak{g}\to M$ into $D\to M$ (or the algebraic analogue of the morphism in the case of $\cal{D}$). The gauged sigma model results from a pullback by this morphism from the Dirac sigma model, which proves to be universal in two-spacetime dimensions in this sense.Comment: 22 pages, 2 figures; To appear in Journal of High Energy Physic

Review of experimental results from SND detector

The review of experimental results obtained with SND detector at VEPP-2M $e^+e^-$ collider in the energy region $\sqrt[]{s}=0.36$ -- 1.38 GeV is given. The presented results include the following items: studies of the light vector mesons radiative decays, OZI-rule and G-parity suppressed $\phi$-meson rare decays, $\phi$-meson parameters measurements, studies of $e^+e^-\to\pi^+\pi^-\pi^0$ process dynamics, $\eta$ and $K_S$ mesons rare decays, $\eta$ and $\phi$ mesons conversion decays, and study of the $e^+e^-$ annihilation into hadrons.Comment: 12 pages and 6 figures. Talk given at the IX International Conference on Hadron Spectroskopy, Protvino, Russia, August 25 - September 1, 200

Evidence of phi --> pi0 pi0 gamma and phi --> pi0 eta gamma decays in SND experiment at VEPP-2M

Preliminary results on the study of e+e- --> phi(1020) --> pi0 pi0 gamma, eta pi0 gamma processes from SND experiment at VEPP-2M collider in Novosibirsk are presented. Branching ratios of rare radiative phi --> pi0 pi0 gamma and phi --> pi0 eta gamma decays are measured: B(phi --> pi0 pi0 gamma ) = (1.1 +- 0.2) * 10^-4 (invariant mass (pi0 pi0) < 800 MeV), B(phi --> eta pi0 gamma ) = (1.3 +- 0.5) * 10^-4.Comment: Talk at the HADRON97 conference, BNL, Aug 24-30 1997; LaTeX, 4 pages, 4 eps figure