ISOCAM-CVF 5-12 mum Spectroscopy of Ultraluminous Infrared Galaxies

2001-01-11

We present low resolution mid infrared spectra of 16 ultraluminous infrared galaxies (ULIRGs) obtained with the CVF spectroscopy mode of ISOCAM on board the Infrared Space Observatory ISO. Our sample completes previous ISO spectroscopy of ultra- and hyperluminous infrared galaxies towards higher luminosities. The combined samples cover an infrared luminosity range of \~10^{12 -13.1} Lo. For about half of the high luminosity ULIRGs studied here, strong aromatic emission bands suggest starburst dominance. Other spectra are dominated by a strong AGN-related continuum with weak superposed emission features of uncertain nature. An improved method to quantitatively characterize the relative contribution of star formation and AGN activity to the mid-infrared emission of ULIRGs is presented. As dominant source of the bolometric luminosity, starbursts prevail at the lower end and AGNs at the higher end of this range. The transition between mostly starburst and mostly AGN powered occurs at ~10^{12.4}$ to $10^{12.5} Lo, and individual luminous starbursts are found up to ~10^{12.65} Lo.

Author(s): Q. D. Tran D. Lutz R. Genzel D. Rigopoulou H. W. W. Spoon E. Sturm M. Gerin D. C. Hines A. F. M. Moorwood D. B. Sanders N. Scoville Y. Taniguchi M. Ward

Ward identities for strongly coupled Eliashberg theories

2004-11-01

We discuss Ward identities for strongly interacting fermion systems described by Eliashberg-type theories. We show that Ward identities are not in conflict with Migdal theorem. We derive diagrammatically Ward identity for a charge vertex in a Fermi liquid, and when a Fermi liquid is destroyed at quantum criticality. We argue that Ward identity for a spin vertex cannot be obtained within Eliashberg theory.

Author(s): Andrey V. Chubukov

Decoherence in quantum walks and quantum computers

2007-11-09

Decoherence is the major stumbling block in the realization of a large-scale quantum computer. Ingenious methods have been devised to overcome decoherence, but their success has been proven only for over-simplified models of system-environment interaction. Whether such methods will be reliable in the face of more realistic models is a fundamental open question. In this partly pedagogical article, we study two toy models of quantum information processing, using the language of \emph{quantum walks}. Decoherence is incorporated in 3 ways - by coupling to a noisy `projective measurement' system, and by coupling to oscillator and spin baths.

Author(s): Andrew P. Hines P. C. E. Stamp

The Screened Field of a Test Particle

2009-12-21

The screened field (forward field and wake) of a test particle moving at constant velocity through an unmagnetized collisionless plasma is calculated analytically and numerically. This paper is based on unpublished material from my MSc thesis, supervised by the late Dr K. C. Hines.

Author(s): R. L. Dewar

Generalization of the event-based Carnevale-Hines integration scheme for integrate-and-fire models

2008-05-12

An event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory synaptic currents and double exponential inhibitory synaptic currents has recently been introduced by Carnevale and Hines. This integration scheme imposes non-physiological constraints on the time constants of the synaptic currents it attempts to model which hamper the general applicability. This paper addresses this problem in two ways. First, we provide physical arguments to show why these constraints on the time constants can be relaxed. Second, we give a formal proof showing which constraints can be abolished. This proof rests on a generalization of the Carnevale-Hines lemma, which is a new tool for comparing double exponentials as they naturally occur in many cascaded decay systems including receptor-neurotransmitter dissociation followed by channel closing. We show that this lemma can be generalized and subsequently used for lifting most of the original constraints on the time constants. Thus we show that the Carnevale-Hines integration scheme for the integrate-and-fire model can be employed for simulating a much wider range of neuron and synapse type combinations than is apparent from the original treatment.

Author(s): Ronald A. J. van Elburg Arjen van Ooyen

Backlund transformations, Ward solitons, and unitons

2004-05-19

The Ward equation, also called the modified 2+1 chiral model, is obtained by a dimension reduction and a gauge fixing from the self-dual Yang-Mills field equation on $R^{2,2}$. It has a Lax pair and is an integrable system. Ward constructed solitons whose extended solutions have distinct simple poles. He also used a limiting method to construct 2-solitons whose extended solutions have a double pole. Ioannidou and Zakrzewski, and Anand constructed more soliton solutions whose extended solutions have a double or triple pole. Some of the main results of this paper are: (i) We construct algebraic B\"acklund transformations (BTs) that generate new solutions of the Ward equation from a given one by an algebraic method. (ii) We use an order $k$ limiting method and algebraic BTs to construct explicit Ward solitons, whose extended solutions have arbitrary poles and multiplicities. (iii) We prove that our construction gives all solitons of the Ward equation explicitly and the entries of Ward solitons must be rational functions in $x, y$ and $t$. (iv) Since stationary Ward solitons are unitons, our method also gives an explicit construction of all $k$-unitons from finitely many rational maps from $C$ to $C^n$.

Author(s): Bo Dai Chuu-Lian Terng

The Cauchy problem of the Ward equation with mixed scattering data

2008-06-03

We solve the Cauchy problem of the Ward equation with both continuous and discrete scattering data.

Author(s): Derchyi Wu

On the Form of Odd Perfect Gaussian Integers

2008-05-14

We extend the sum-of-divisors function to the complex plane via the Gaussian integers. Then we prove a modified form of Euler's classification of odd perfect numbers.

Author(s): Matthew Ward

Polynomial Zsigmondy theorems

2010-02-25

We find analogues of the primitive divisor results of Zsigmondy, Bang, Bilu-Hanrot-Voutier, and Carmichael in polynomial rings, following the methods of Carmichael.

Author(s): Anthony Flatters Thomas Ward

Correlation functions from two-dimensional string Ward identities

1992-04-16

We rederive the $w_\infty$ Ward identities, starting from the existence of trivial linearized gauge invariances, and using the method of canceled propagators in the operator formalism. Recursion relations for certain classes of correlation functions are derived, and these correlation function are calculated exactly. We clarify the relation of these results with another derivation of the Ward identities, which relies directly on charge conservation. We also emphasize the importance of the kinematics of canceled propagators in ensuring that the Ward identities are non-trivial. Finally, we sketch an extension of Ward identities to open strings.

Author(s): Igor R. Klebanov Andrea Pasquinucci

The Polarized Spectrum of Apm 08279+5255

1999-02-04

We report the discovery of significant linear polarization (p > 1%) in the hyperluminous z=3.87 BALQSO APM~08279+5255. The polarization spectrum is complex, with properties similar to those of other, lower redshift but more highly polarized BALQSOs. The resonance emission lines are unpolarized while the absorption troughs show polarization similar to or higher than the continuum. In particular, an apparent increase of polarization in the trough covering 1000-1030 angstroms (rest) supports the interpretation of this feature as a broad absorption component associated with OVI/Ly_beta local to the QSO, as opposed to an intervening damped Ly_alpha absorption system. The elevated polarization in some of the absorption features implies that we view the scattered (polarized) spectrum through a sightline with less absorbing material than the direct spectrum. Therefore, the complex structure of the polarization spectrum in this brilliant lensed BALQSO suggests that it will be an important laboratory for studying the structure of QSOs at high redshift.

Author(s): Dean C. Hines Gary D. Schmidt Paul S. Smith

NICMOS Observations of the Pre-Main-Sequence Planetary Debris System HD 98800

1999-05-27

Spectral energy distributions (SEDs) from 0.4 to 4.7 microns are presented for the two principal stellar components of HD~98800, A and B. The third major component, an extensive planetary debris system (PDS), emits > 20% of the luminosity of star B in a blackbody SED at 164 +/- 5K extending from mid-IR to millimeter-wavelengths. At 0.95 microns a preliminary upper limit of < 0.06 is obtained for the ratio of reflected light to the total from star B. This result limits the albedo of the PDS to < 0.3. Values are presented for the temperature, luminosity, and radius of each major systemic component. Remarkable similarities are found between the PDS and the interplanetary debris system around the Sun as it could have appeared a few million years after its formation.

Author(s): Frank J. Low Dean C. Hines Glenn Schneider

Spitzer Observations of High Redshift QSOs

2006-04-17

We have observed 13 z >= 4.5 QSOs using the Multiband Imaging Photometer for Spitzer, nine of which were also observed with the Infrared Array Camera. The observations probe rest wavelengths ~ 0.6-4.3 micron, bracketing the local minimum in QSO spectral energy distributions (SEDs) between strong optical emission associated directly with accretion processes and thermal emission from hot dust heated by the central engine. The new Spitzer photometry combined with existing measurements at other wavelengths shows that the SEDs of high redshift QSOs (z >= 4.5) do not differ significantly from typical QSOs of similar luminosity at lower redshifts (z <~ 2). This behavior supports other indications that all the emission components and physical structures that characterize QSO activity can be established by z = 6.4. The similarity also suggests that some QSOs at high redshift will be very difficult to identify because they are viewed along dust-obscured sight lines.

Author(s): D. C. Hines O. Krause G. H. Rieke X. Fan M. Blaylock G. Neugebauer

Symmetries and transitions of bounded Turing machines

1998-12-16

We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic automata, then (non-deterministic) two-way automata and bounded Turing machines --- that is, Turing machines where the read / write head is unable to move past the end of the input word. In the case of two-way automata, the transition monoids generalise to endomorphism monoids in compact closed categories. These use Girard's resolution formula (from the Geometry of Interaction representation of linear logic) to construct the images of singleton words. In the case of bounded Turing machines, the transition homomorphism generalises to a monoid homomorphism from the natural numbers to a monoid constructed from the union of endomorphism monoids of a compact closed category, together with an appropriate composition. These use Girard's execution formula (also from the Geometry of Interaction representation of linear logic) to construct images of singletons.

Author(s): Peter M. Hines

Entanglement of two-mode Bose-Einstein condensates

2002-09-24

We investigate the entaglement characteristics of two general bimodal Bose-Einstein condensates - a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and thus the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.

Author(s): Andrew P. Hines Ross H. McKenzie Gerard J. Milburn

Quantum entanglement and fixed-point bifurcations

2003-08-29

How does the classical phase space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state - the ground state - achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

Author(s): Andrew P. Hines G. J. Milburn Ross H. McKenzie

Entanglement and bifurcations in Jahn-Teller models

2004-02-03

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The $E\otimes\beta$ system models the coupling of a two-level electronic system, or qubit, to a single oscillator mode, while the $E\otimes\epsilon$ models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the $E\otimes\beta$ system, the ground states of the $E\otimes\epsilon$ model always exhibit entanglement. For the $E\otimes\beta$ case we aim to clarify results from previous work, alluding to a link between the ground state entanglement characteristics and a bifurcation of a fixed point in the classical analogue. In the $E\otimes\epsilon$ case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.

Author(s): Andrew P. Hines Christopher M. Dawson Ross H. McKenzie G. J. Milburn

Entanglement Sharing and Decoherence in the Spin-Bath

2004-07-27

The monogamous nature of entanglement has been illustrated by the derivation of entanglement sharing inequalities - bounds on the amount of entanglement that can be shared amongst the various parts of a multipartite system. Motivated by recent studies of decoherence, we demonstrate an interesting manifestation of this phenomena that arises in system-environment models where there exists interactions between the modes or subsystems of the environment. We investigate this phenomena in the spin-bath environment, constructing an entanglement sharing inequality bounding the entanglement between a central spin and the environment in terms of the pairwise entanglement between individual bath spins. The relation of this result to decoherence will be illustrated using simplified system-bath models of decoherence.

Author(s): Christopher M. Dawson Andrew P. Hines Ross H. McKenzie G. J. Milburn

Quantum Walks, Quantum Gates and Quantum Computers

2007-01-14

The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between quantum walk Hamiltonians and Hamiltonians for qubit systems and quantum circuits; this is done for both a single- and multi-excitation coding, and for more general mappings. Specific examples of spin chains, as well as static and dynamic systems of qubits, are mapped to quantum walks, and walks on hyperlattices and hypercubes are mapped to various gate systems. We also show how to map a quantum circuit performing the quantum Fourier transform, the key element of Shor's algorithm, to a quantum walk system doing the same. The results herein are an essential preliminary to a Hamiltonian formulation of quantum walks in which coupling to a dynamic quantum environment is included.

Author(s): Andrew P. Hines P. C. E. Stamp

Comparing three models of attack and failure tolerance in electric power networks

2010-02-11

In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in power systems, we measure the susceptibility of power networks to random failures and directed attacks using three measures of vulnerability: characteristic path lengths, connectivity loss and blackout sizes. The first two are purely topological measures, following the procedure described by Albert et al. (2004). The blackout size calculation results from a simplified model of cascading failure in power networks. Tests with randomly selected sections of the Eastern US power grid indicate that in topological dynamics power grids are similar to random graphs, which is to be expected given the observed exponential degree distribution. However the connectivity loss model and the cascading failure model indicate that power grids behave more like scale free networks, in that they are acutely more vulnerable to directed attacks than random failures. These results suggest caution in drawing conclusions about grid vulnerability from simple topological metrics.

Author(s): P. Hines E. Cotilla-Sanchez S. Blumsack