On birational involutions of P3P^3

Let $X$ be a rationally connected three-dimensional algebraic variety and let $\tau$ be an element of order two in the group of its birational selfmaps. Suppose that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program we give a rough classification of such elements.Comment: 24 pages, late

Uncertainty relations in curved spaces

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in details. The investigation can be of interest for string and brane theory, solid state physics (quantum wires) and quantum optics.Comment: published version; phase space structure discussion adde

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

Nonlinear interaction of light with Bose-Einstein condensate: new methods to generate subpoissonian light

We consider $\Lambda$-type model of the Bose-Einstein condensate of sodium atoms interacting with the light. Coefficients of the Kerr-nonlinearity in the condensate can achieve large and negative values providing the possibility for effective control of group velocity and dispersion of the probe pulse. We find a regime when the observation of the "slow" and "fast" light propagating without absorption becomes achievable due to strong nonlinearity. An effective two-level quantum model of the system is derived and studied based on the su(2) polynomial deformation approach. We propose an efficient way for generation of subpoissonian fields in the Bose-Einstein condensate at time-scales much shorter than the characteristic decay time in the system. We show that the quantum properties of the probe pulse can be controlled in BEC by the classical coupling field.Comment: 13 pages, 6 figures, 1 tabl

Probing the ground state in gauge theories

We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string description is better in the confined phase but the Coulombic description is best in the deconfined phase; the last result is shown to agree with analytical calculations. Surprisingly in the non-abelian theory the Coulombic description is better in both the Higgs and confined phases. This indicates a significant difference in the width of the flux tubes in the two theories.Comment: 13 pages, 10 .eps figures. V2: conclusions extende

Charges in Gauge Theories

In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the Abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green's functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions.Comment: 47 pages, LaTeX, 14 figures, uses feynmp, necessary Metapost files included. Review to appear in Pramana, Journal of Physics. Minor LaTeX change to make page numbers visible on "Letter" paper forma

Galactic Binary Gravitational Wave Noise within LISA Frequency Band

Gravitational wave noise associated with unresolved binary stars in the Galaxy is studied with the special aim of determining the upper frequency at which it stops to contribute at the rms noise level of the proposed space-born interferometer (LISA). The upper limit to this background is derived from the statistics of SN Ia explosions, part of which can be triggered by binary white dwarf coalescences. The upper limiting frequency at which binary stochastic noise crosses LISA rms sensitivity is found to lie within the range 0.03-0.07 Hz, depending on the galactic binary white dwarf coalescence rate. To be reliably detectable by LISA, the energy density of relic cosmological background per logarithmic frequency interval should be Omega_{GW}h_{100}^2>10^{-8} at f>0.03 Hz.Comment: 16 pages with 1 eps figure, aasms4.sty, to appear in the ApJ vol. 494 February 20, 1998 issu

Survival through networks: the 'grip' of the administrative links in the Russian post-Soviet context

© 2014 Taylor & Francis. Based on an analysis of the post-Soviet transformation experience of four defence sector organizations in a Russian region where the defence sector occupies a substantial part of the local economy, this article develops a typology of network relationships: Grooved Inter-relationship Patterns (Gr’ip) networks and Fluid Inter-relationship Patterns (Fl’ip) networks. This typology can be applied to a range of transition/emerging market and low system trust contexts. Gr’ip networks, in this case, represent the persisting legacy of the Soviet command-administrative system. Fl’ip networks are here an attempt by the defence companies to link into the civilian supply chains of a developing market economy. This article argues that Gr’ip networks had and still have a crucial role to play in Russian enterprises’ survival and development

Broad-band gravitational-wave pulses from binary neutron stars in eccentric orbits

Maximum gravitational wave emission from binary stars in eccentric orbits occurs near the periastron passage. We show that for a stationary distribution of binary neutron stars in the Galaxy, several high-eccentricity systems with orbital periods in the range from tens of minutes to several days should exist that emit broad gravitational-wave pulses in the frequency range 1-100 mHz. The space interferometer LISA could register the pulsed signal from these system at a signal-to-noise ratio level $S/N>5\sqrt{5}$ in the frequency range $\sim 10^{-3}-10^{-1}$ Hz during one-year observational time. Some detection algorithms for such a signal are discussed.Comment: 17 pages, LATEX, 3 figures, Astronomy Letters, 2002, in press; typos corrected, refference adde