Dissipation time and decay of correlations

We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and its associated propagators: spectral properties, local expansivity, and global mixing properties. We show that the dissipation is slow for a general class of non-weakly-mixing maps; on the opposite, it is fast for a large class of exponentially mixing systems which include uniformly expanding maps and Anosov diffeomorphisms.Comment: 26 Pages, LaTex. Submitted to Nonlinearit

Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field

We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly non-equilibrium plasmas of solar systems and thermonuclear devices. We solve fractional kinetic equations, study the properties of the solution, and compare analytical results with those of numerical simulation based on the solution of the Langevin equations with the noise source having Levy stable probability density. We found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.Comment: 15 pages, LaTeX, 5 figures PostScrip

On Physical Equivalence between Nonlinear Gravity Theories

We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199

Light-Front Quantisation as an Initial-Boundary Value Problem

In the light front quantisation scheme initial conditions are usually provided on a single lightlike hyperplane. This, however, is insufficient to yield a unique solution of the field equations. We investigate under which additional conditions the problem of solving the field equations becomes well posed. The consequences for quantisation are studied within a Hamiltonian formulation by using the method of Faddeev and Jackiw for dealing with first-order Lagrangians. For the prototype field theory of massive scalar fields in 1+1 dimensions, we find that initial conditions for fixed light cone time {\sl and} boundary conditions in the spatial variable are sufficient to yield a consistent commutator algebra. Data on a second lightlike hyperplane are not necessary. Hamiltonian and Euler-Lagrange equations of motion become equivalent; the description of the dynamics remains canonical and simple. In this way we justify the approach of discretised light cone quantisation.Comment: 26 pages (including figure), tex, figure in latex, TPR 93-

Leaving the ISCO: the inner edge of a black-hole accretion disk at various luminosities

The "radiation inner edge" of an accretion disk is defined as the inner boundary of the region from which most of the luminosity emerges. Similarly, the "reflection edge" is the smallest radius capable of producing a significant X-ray reflection of the fluorescent iron line. For black hole accretion disks with very sub-Eddington luminosities these and all other "inner edges" locate at ISCO. Thus, in this case, one may rightly consider ISCO as the unique inner edge of the black hole accretion disk. However, even for moderate luminosities, there is no such unique inner edge as differently defined edges locate at different places. Several of them are significantly closer to the black hole than ISCO. The differences grow with the increasing luminosity. For nearly Eddington luminosities, they are so huge that the notion of the inner edge losses all practical significance.Comment: 12 pages, 15 figures, submitted to A&

<i>Spitzer</i> microlens measurement of a massive remnant in a well-separated binary

We report the detection and mass measurement of a binary lens OGLE-2015-BLG-1285La,b, with the more massive component having M1 > 1.35 M⊙ (80% probability). A main-sequence star in this mass range is ruled out by limits on blue light, meaning that a primary in this mass range must be a neutron star (NS) or black hole (BH). The system has a projected separation r⊥ = 6.1 ± 0.4 AU and lies in the Galactic bulge. These measurements are based on the "microlens parallax" effect, i.e., comparing the microlensing light curve as seen from Spitzer, which lay at 1.25 AU projected from Earth, to the light curves from four ground-based surveys, three in the optical and one in the near-infrared. Future adaptive optics imaging of the companion by 30 m class telescopes will yield a much more accurate measurement of the primary mass. This discovery both opens the path and defines the challenges to detecting and characterizing BHs and NSs in wide binaries, with either dark or luminous companions. In particular, we discuss lessons that can be applied to future Spitzer and Kepler K2 microlensing parallax observations

Static Friction Phenomena in Granular Materials: Coulomb Law vs. Particle Geometry

The static as well as the dynamic behaviour of granular material are determined by dynamic {\it and} static friction. There are well known methods to include static friction in molecular dynamics simulations using scarcely understood forces. We propose an Ansatz based on the geometrical shape of nonspherical particles which does not involve an explicit expression for static friction. It is shown that the simulations based on this model are close to experimental results.Comment: 11 pages, Revtex, HLRZ-33/9

Group analysis of structure equations for stars in radiative and convective equilibrium

It is proposed to use the Lie group theory of symmetries of differential equations to investigate the system of equations describing a static star in a radiative and convective equilibrium. It is shown that the action of an admissible group induces a certain algebraic structure in the set of all solutions, which can be used to find a family of new solutions. We have demonstrated that, in the most general case, the equations admit an infinite parameter group of quasi-homologous transformations. We have found invariants of the symmetries group which correspond to the fundamental relations describing a physical characteristic of the stars such as the Hertzsprung-Russell diagram or the mass-luminosity relation. In this way we can suggest that group invariants have not only purely mathematical sense, but their forms are closely associated with the basic empirical relations.Comment: LaTeX2e, 13page

Herschel/HIFI observations of interstellar OH+ and H2O+ towards W49N: a probe of diffuse clouds with a small molecular fraction

We report the detection of absorption by interstellar hydroxyl cations and water cations, along the sight-line to the bright continuum source W49N. We have used Herschel's HIFI instrument, in dual beam switch mode, to observe the 972 GHz N = 1 - 0 transition of OH+ and the 1115 GHz 1(11) - 0(00) transition of ortho-H2O+. The resultant spectra show absorption by ortho-H2O+, and strong absorption by OH+, in foreground material at velocities in the range 0 to 70 km/s with respect to the local standard of rest. The inferred OH+/H2O+ abundance ratio ranges from ~ 3 to ~ 15, implying that the observed OH+ arises in clouds of small molecular fraction, in the 2 - 8% range. This conclusion is confirmed by the distribution of OH+ and H2O+ in Doppler velocity space, which is similar to that of atomic hydrogen, as observed by means of 21 cm absorption measurements, and dissimilar from that typical of other molecular tracers. The observed OH+/H abundance ratio of a few E-8 suggests a cosmic ray ionization rate for atomic hydrogen of (0.6 - 2.4) E-16 s-1, in good agreement with estimates inferred previously for diffuse clouds in the Galactic disk from observations of interstellar H3+ and other species.Comment: Accepted for publication in A&A Letter

Measurement of the production cross section for W-bosons in association with jets in pp collisions at s=7 TeV with the ATLAS detector

This Letter reports on a first measurement of the inclusive W + jets cross section in proton-proton collisions at a centre-of-mass energy of 7 TeV at the LHC, with the ATLAS detector. Cross sections, in both the electron and muon decay modes of the W-boson, are presented as a function of jet multiplicity and of the transverse momentum of the leading and next-to-leading jets in the event. Measurements are also presented of the ratio of cross sections sigma (W + >= n)/sigma(W + >= n - 1) for inclusive jet multiplicities n = 1-4. The results, based on an integrated luminosity of 1.3 pb(-1), have been corrected for all known detector effects and are quoted in a limited and well-defined range of jet and lepton kinematics. The measured cross sections are compared to particle-level predictions based on perturbative QCD. Next-to-leading order calculations, studied here for n <= 2, are found in good agreement with the data. Leading-order multiparton event generators, normalized to the NNLO total cross section, describe the data well for all measured jet multiplicitie