Trace formulas for stochastic evolution operators: Smooth conjugation method

The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighborhood of a given saddlepoint exactly by means of a smooth conjugacy, a locally analytic nonlinear change of field variables. The perturbative corrections are transfered to the corresponding Jacobian, which we expand in terms of the conjugating function, rather than the action used in defining the path integral. The new perturbative expansion which follows by a recursive evaluation of derivatives appears more compact than the standard Feynman diagram perturbation theory. The result is a stochastic analog of the Gutzwiller trace formula with the ``hbar'' corrections computed an order higher than what has so far been attainable in stochastic and quantum-mechanical applications.Comment: 16 pages, 1 figure, New techniques and results for a problem we considered in chao-dyn/980703

Recent progress in Hamiltonian light-front QCD

Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. We outline our approach and discuss the computational challenges.Comment: Invited paper at Light Cone 2008, Mulhouse, Franc

Quantum communication using a bounded-size quantum reference frame

Typical quantum communication schemes are such that to achieve perfect decoding the receiver must share a reference frame with the sender. Indeed, if the receiver only possesses a bounded-size quantum token of the sender's reference frame, then the decoding is imperfect, and we can describe this effect as a noisy quantum channel. We seek here to characterize the performance of such schemes, or equivalently, to determine the effective decoherence induced by having a bounded-size reference frame. We assume that the token is prepared in a special state that has particularly nice group-theoretic properties and that is near-optimal for transmitting information about the sender's frame. We present a decoding operation, which can be proven to be near-optimal in this case, and we demonstrate that there are two distinct ways of implementing it (corresponding to two distinct Kraus decompositions). In one, the receiver measures the orientation of the reference frame token and reorients the system appropriately. In the other, the receiver extracts the encoded information from the virtual subsystems that describe the relational degrees of freedom of the system and token. Finally, we provide explicit characterizations of these decoding schemes when the system is a single qubit and for three standard kinds of reference frame: a phase reference, a Cartesian frame (representing an orthogonal triad of spatial directions), and a reference direction (representing a single spatial direction).Comment: 17 pages, 1 figure, comments welcome; v2 published versio

Excited OH+, H2O+, and H3O+ in NGC 4418 and Arp 220

We report on Herschel/PACS observations of absorption lines of OH+, H2O+ and H3O+ in NGC 4418 and Arp 220. Excited lines of OH+ and H2O+ with E_lower of at least 285 and \sim200 K, respectively, are detected in both sources, indicating radiative pumping and location in the high radiation density environment of the nuclear regions. Abundance ratios OH+/H2O+ of 1-2.5 are estimated in the nuclei of both sources. The inferred OH+ column and abundance relative to H nuclei are (0.5-1)x10^{16} cm-2 and \sim2x10^{-8}, respectively. Additionally, in Arp 220, an extended low excitation component around the nuclear region is found to have OH+/H2O+\sim5-10. H3O+ is detected in both sources with N(H3O+)\sim(0.5-2)x10^{16} cm-2, and in Arp 220 the pure inversion, metastable lines indicate a high rotational temperature of ~500 K, indicative of formation pumping and/or hot gas. Simple chemical models favor an ionization sequence dominated by H+ - O+ - OH+ - H2O+ - H3O+, and we also argue that the H+ production is most likely dominated by X-ray/cosmic ray ionization. The full set of observations and models leads us to propose that the molecular ions arise in a relatively low density (\gtrsim10^4 cm-3) interclump medium, in which case the ionization rate per H nucleus (including secondary ionizations) is zeta>10^{-13} s-1, a lower limit that is severalx10^2 times the highest rate estimates for Galactic regions. In Arp 220, our lower limit for zeta is compatible with estimates for the cosmic ray energy density inferred previously from the supernova rate and synchrotron radio emission, and also with the expected ionization rate produced by X-rays. In NGC 4418, we argue that X-ray ionization due to an AGN is responsible for the molecular ion production.Comment: 24 pages, 13 figures. Accepted for publication in Astronomy & Astrophysic

A Close Look at Star Formation around Active Galactic Nuclei

We analyse star formation in the nuclei of 9 Seyfert galaxies at spatial resolutions down to 0.085arcsec, corresponding to length scales of less than 10pc in some objects. Our data were taken mostly with the near infrared adaptive optics integral field spectrograph SINFONI. The stellar light profiles typically have size scales of a few tens of parsecs. In two cases there is unambiguous kinematic evidence for stellar disks on these scales. In the nuclear regions there appear to have been recent - but no longer active - starbursts in the last 10-300Myr. The stellar luminosity is less than a few percent of the AGN in the central 10pc, whereas on kiloparsec scales the luminosities are comparable. The surface stellar luminosity density follows a similar trend in all the objects, increasing steadily at smaller radii up to 10^{13}L_sun/kpc^2 in the central few parsecs, where the mass surface density exceeds 10^4M_sun/pc^2. The intense starbursts were probably Eddington limited and hence inevitably short-lived, implying that the starbursts occur in multiple short bursts. The data hint at a delay of 50--100Myr between the onset of star formation and subsequent fuelling of the black hole. We discuss whether this may be a consequence of the role that stellar ejecta could play in fuelling the black hole. While a significant mass is ejected by OB winds and supernovae, their high velocity means that very little of it can be accreted. On the other hand winds from AGB stars ultimately dominate the total mass loss, and they can also be accreted very efficiently because of their slow speeds.Comment: 51 pages, including 27 figures; accepted by ApJ (paper reorganised, but results & conclusions the same

Remark on charge conjugation in the non relativistic limit

We study the non relativistic limit of the charge conjugation operation $\cal C$ in the context of the Dirac equation coupled to an electromagnetic field. The limit is well defined and, as in the relativistic case, $\cal C$, $\cal P$ (parity) and $\cal T$ (time reversal) are the generators of a matrix group isomorphic to a semidirect sum of the dihedral group of eight elements and $\Z_2$. The existence of the limit is supported by an argument based in quantum field theory. Also, and most important, the limit exists in the context of galilean relativity. Finally, if one complexifies the Lorentz group and therefore the galilean spacetime $x_\mu$, then the explicit form of the matrix for $\cal C$ allows to interpret it, in this context, as the complex conjugation of the spatial coordinates: $\vec{x} \to \vec{x}^*$. This result is natural in a fiber bundle description.Comment: 8 page

Spitzer Quasar and ULIRG evolution study (QUEST): I. The origin of the far infrared continuum of QSOs

This paper addresses the origin of the far-infrared (FIR) continuum of QSOs, based on the Quasar and ULIRG Evolution Study (QUEST) of nearby QSOs and ULIRGs using observations with the Spitzer Space Telescope. For 27 Palomar-Green QSOs at z <~ 0.3, we derive luminosities of diagnostic lines ([NeII]12.8um, [NeV]14.3um, [OIV]25.9um) and emission features (PAH7.7um emission which is related to star formation), as well as continuum luminosities over a range of mid- to far-infrared wavelengths between 6 and 60um. We detect star-formation related PAH emission in 11/26 QSOs and fine-structure line emission in all of them, often in multiple lines. The detection of PAHs in the average spectrum of sources which lack individual PAH detections provides further evidence for the widespread presence of PAHs in QSOs. Similar PAH/FIR and [NeII]/FIR ratios are found in QSOs and in starburst-dominated ULIRGs and lower luminosity starbursts. We conclude that the typical QSO in our sample has at least 30% but likely most of the far-infrared luminosity (~ 10^(10...12)Lsun) arising from star formation, with a tendency for larger star formation contribution at the largest FIR luminosities. In the QSO sample, we find correlations between most of the quantities studied including combinations of AGN tracers and starburst tracers. The common scaling of AGN and starburst luminosities (and fluxes) is evidence for a starburst-AGN connection in luminous AGN. Strong correlations of far-infrared continuum and starburst related quantities (PAH, low excitation [NeII]) offer additional support for the starburst origin of far-infrared emission.Comment: 39 pages, 8 figures, accepted for publication in Ap

Quantum walks with infinite hitting times

Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition, which for discrete time quantum walks is that the degeneracy of the evolution operator be greater than the degree of the graph. The set of initial states which give an infinite hitting time form a subspace. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. In the case of the discrete walk, if this condition is satisfied the walk will have infinite hitting times for any choice of a coin operator, and we give a class of graphs with infinite hitting times for any choice of coin. Hitting times are not very well-defined for continuous time quantum walks, but we show that the idea of infinite hitting-time walks naturally extends to the continuous time case as well.Comment: 28 pages, 3 figures in EPS forma

A Bogomol`nyi equation for intersecting domain walls

We argue that the Wess-Zumino model with quartic superpotential admits static solutions in which three domain walls intersect at a junction. We derive an energy bound for such junctions and show that configurations saturating it preserve 1/4 supersymmetry.Comment: 4 pages revtex. No figures. Revised version to appear in Physical Review Letters includes discussion of the supersymmetry algebr

The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation

In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. An alternative, less well-known decomposition, into the completely symmetric part S of C plus the reminder A, turns out to be irreducible under the 3-dimensional general linear group. We show that the SA-decomposition is unique, irreducible, and preserves the symmetries of the elasticity tensor. The MN-decomposition fails to have these desirable properties and is such inferior from a physical point of view. Various applications of the SA-decomposition are discussed: the Cauchy relations (vanishing of A), the non-existence of elastic null Lagrangians, the decomposition of the elastic energy and of the acoustic wave propagation. The acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The Cauchy part governs the longitudinal wave propagation. We provide explicit examples of the effectiveness of the SA-decomposition. A complete class of anisotropic media is proposed that allows pure polarizations in arbitrary directions, similarly as in an isotropic medium.Comment: 1 figur