Generalized Lenard Chains, Separation of Variables and Superintegrability

We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional \omega N manifold guarantees the separation of variables. As an application, we construct such chains for the H\'enon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.Comment: 14 pages Revte

Crossovers in the Two Dimensional Ising Spin Glass with ferromagnetic next-nearest-neighbor interactions

By means of extensive computer simulations we analyze in detail the two dimensional $\pm J$ Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to ``spin glass'' like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the ``spin glass'' behavior to a paramagnetic phase for the largest volume studied.Comment: 19 pages with 9 postscript figures also available at http://chimera.roma1.infn.it/index_papers_complex.html. Some changes in captions of figures 1 and

Generation of different Bell states within the SPDC phase-matching bandwidth

We study the frequency-angular lineshape for a phase-matched nonlinear process producing entangled states and show that there is a continuous variety of maximally-entangled states generated for different mismatch values within the natural bandwidth. Detailed considerations are made for two specific methods of polarization entanglement preparation, based on type-II spontaneous parametric down-conversion (SPDC) and on SPDC in two subsequent type-I crystals producing orthogonally polarized photon pairs. It turns out that different Bell states are produced at the center of the SPDC line and on its slopes, corresponding to about half-maximum intensity level. These Bell states can be filtered out by either frequency selection or angular selection, or both. Our theoretical calculations are confirmed by a series of experiments, performed for the two above-mentioned schemes of producing polarization-entangled photon pairs and with two kinds of measurements: frequency-selective and angular-selective.Comment: submitted for publicatio

Scale Invariance in disordered systems: the example of the Random Field Ising Model

We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not self-averaging. This is due to the formation of a bound state in the underlying field theory. We argue that this non perturbative phenomenon is not particular to the RFIM in 3-d. It is generic for disordered systems in two dimensions and may also happen in other three dimensional disordered systems

The CERN Cryogenic Test Facility for the Atlas Barrel Toroid Magnets

The superconducting magnet system of the ATLAS detector will consist of a central solenoid, two end-cap toroidal magnets (ECT) and the barrel toroid magnet (BT) made of eight coils symmetrically placed around the central axis of the detector. The magnets will be tested individually in a 5000 m2 experimental area prior to their final installation at an underground cavern of the LHC Collider. For the BT magnets, a dedicated cryogenic test facility has been designed which is currently under the construction and commissioning phase. A liquid nitrogen pre-cooling unit and a 1200 [email protected] refrigerator will allow flexible operating conditions via a rather complex distribution and transfer line system. Flow of two-phase helium for cooling the coils is provided by centrifugal pumps immersed in a saturated liquid helium bath. The integration of the pumps in an existing cryostat required the adoption of novel mechanical solutions. Tests conducted permitted the validation of the technical design of the cryostat and its instrumentation. The characteristics of one pump were measured and pressure rise of 300 mbar at nominal flow of 80 g/s confirmed the specifications

Can Gravity Distinguish Between Dirac and Majorana Neutrinos?

We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavour system, as shown explicitly for SN1987A.Comment: 4 pages, 2 figures; minor changes of text; typo corrected; accepted in Physical Review Letter

Resonant Absorption in the AGN spectra emerging from photoionized gas: differences between steep and flat ionizing continua

We present photoionization models accounting for both photoelectric and resonant absorption. Resonance absorption lines from C, O, Ne, Mg, Si S and Fe between 0.1 and 10 keV are treated. In particular we consider the complex of almost 60 strong Fe L absorption lines around 1 keV. We calculate profiles, intensities and equivalent widths of each line, considering both Doppler and natural broadening mechanisms. Doppler broadening includes a term accounting for turbulence of the gas along the line of sight. We computed spectra transmitted by gas illuminated by drastically different ionizing continua and compared them to spectra observed in flat X-ray spectrum, broad optical emission line type 1 AGN, and steep X-ray spectrum, narrow optical emission line type 1 AGN. We show that the $\sim 1$ keV absorption feature observed in moderate resolution X-ray spectra of several Narrow Line Seyfert 1 galaxies can be explained by photoionization models, taking into account for resonance absorption, without requiring relativistic outflowing velocities of the gas, if the physical properties of these absorbers are close to those found in flat X-ray spectrum Seyfert 1 galaxies.Comment: 22 pages, 10 figures. Accepted for publication on Ap

Weak Reprocessed Features in the Broad Line Radio Galaxy 3C382

We present a detailed X-ray study of the Broad Line Radio Galaxy 3C382, observed with the BeppoSAX satellite in a very bright state. The continuum emission is well modeled with a power law that steepens at high energies, with an e-folding energy of about 120 keV. At soft energies a clear excess of emission is detected, which can not be explained solely by the extended thermal halo seen in a ROSAT HRI image. A second, more intense soft X-ray component, possibly related to an accretion disk, is required by the data. Both a reflection component (R=0.3) and an iron line (EW \sim 50) are detected, at levels much weaker than in Seyfert galaxies, suggesting a common origin. Combining our measurements with results from the literature we find that the iron line has remained approximately constant over 9 years while the continuum varied by a factor of 5. Thus the fluorescent gas does not respond promptly to the variations of the X-ray primary source, suggesting that the reprocessing site is located away, likely at parsec distances. While the continuum shape indicates that X-rays derive from a thermal Comptonization process, the weakness of other spectral features implies that either the upper layers of the optically thick accretion disk are completely ionized or the corona above the disk is outflowing with mildly relativistic velocity.Comment: 11 pages, 4 figures. Accepted for publication in the Astrophysical Journa

Distribution of roots of random real generalized polynomials

The average density of zeros for monic generalized polynomials, $P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like $|\hbox{\rm Im}\,z|$. We present the low and high disorder asymptotic behaviors. Then we particularize to the large $n$ limit of the average density of complex roots of monic algebraic polynomials of the form $P_n(z) = z^n +\sum_{k=1}^{n}c_kz^{n-k}$ with real independent, identically distributed Gaussian coefficients having zero mean and dispersion $\delta = \frac 1{\sqrt{n\lambda}}$. The average density tends to a simple, {\em universal} function of $\xi={2n}{\log |z|}$ and $\lambda$ in the domain $\xi\coth \frac{\xi}{2}\ll n|\sin \arg (z)|$ where nearly all the roots are located for large $n$.Comment: 17 pages, Revtex. To appear in J. Stat. Phys. Uuencoded gz-compresed tarfile (.66MB) containing 8 Postscript figures is available by e-mail from [email protected]