Encoding algebraic power series

Algebraic power series are formal power series which satisfy a univariate polynomial equation over the polynomial ring in n variables. This relation determines the series only up to conjugacy. Via the Artin-Mazur theorem and the implicit function theorem it is possible to describe algebraic series completely by a vector of polynomials in n+p variables. This vector will be the code of the series. In the paper, it is then shown how to manipulate algebraic series through their code. In particular, the Weierstrass division and the Grauert-Hironaka-Galligo division will be performed on the level of codes, thus providing a finite algorithm to compute the quotients and the remainder of the division.Comment: 35 page

Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate

We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a `coherent' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power law) or rapid (Gaussian) decoherence of the mean values themselves.Comment: 4 pages, 3 figures, lette

Multi-wavelength Observations of the Giant X-ray Flare Galaxy NGC 5905: signatures of tidal disruption

NGC 5905 is one of the few galaxies with no prior evidence for an AGN in which an X-ray flare, due to the tidal disruption of a star by the massive black hole in the center of the galaxy, was detected by the RASS in 1990-91. Here we present analysis of late-time follow-up observations of NGC 5905 using Chandra, Spitzer VLA 3 GHz and 8 GHz archival data and GMRT 1.28 GHz radio observations. The X-ray image shows no compact source that could be associated with an AGN. Instead, the emission is extended -- likely due to nuclear star formation and the total measured X-ray luminosity is comparable to the X-ray luminosity determined from the 2002 Chandra observations. Diffuse X-ray emission was detected close to the circum-nuclear star forming ring. The Spitzer 2006 mid-infrared spectrum also shows strong evidence of nuclear star formation but no clear AGN signatures. The semi-analytical models of Tommasin et. al. 2010 together with the measured [OIV]/[NeII] line ratio suggest that at most only 5.6% of the total IR Flux at 19 $\mu$m is being contributed by the AGN. The GMRT 1.28 GHz observations reveal a nuclear source. In the much higher resolution VLA 3 GHz map, the emission has a double lobed structure of size 2.7'' due to the circumnuclear star forming ring. The GMRT 1.28 GHz peak emission coincides with the center of the circumnuclear ring. We did not detect any emission in the VLA 8 GHz (1996) archival data. The 3 $\sigma$ upper limits for the radio afterglow of the TDE at 1.28 GHz, 3 GHz and 8 GHz are 0.17 mJy, 0.09 mJy and 0.09 mJy, respectively. Our studies thus show that (i) NGC 5905 has a declining X-ray flux consistent with a TDE, (ii) the IR flux is dominated by nuclear star formation, (iii) the nuclear radio emission observed from the galaxy is due to circumnuclear star formation, (iv) no compact radio emission associated with a radio afterglow from the TDE is detected.Comment: 12 pages, 8 figures, accepted to be published in Astrophysics and Space Scienc

Quantal Consequences of Perturbations Which Destroy Structurally Unstable Orbits in Chaotic Billiards

Non-generic contributions to the quantal level-density from parallel segments in billiards are investigated. These contributions are due to the existence of marginally stable families of periodic orbits, which are structurally unstable, in the sense that small perturbations, such as a slight tilt of one of the segments, destroy them completely. We investigate the effects of such perturbation on the corresponding quantum spectra, and demonstrate them for the stadium billiard

Hyper-chaotic magnetisation dynamics of two interacting dipoles

The present work is a numerical study of the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of a time-dependent external magnetic field using the Landau–Lifshitz equation. Particles are coupled through the dipole–dipole interaction. The applied magnetic field is made of a constant longitudinal amplitude component and a time-dependent transversal amplitude component. Dynamical states obtained are represented by their Lyapunov exponents and bifurcation diagrams. The dependence on the largest and the second largest Lyapunov exponents, as a function of the magnitude and frequency of the applied magnetic field, and the relative distance between particles, is studied. The system presents multiple transitions between regular and chaotic behaviour depending on the control parameters. In particular, the system presents consistent hyper-chaotic states