Generalized definition of time delay in scattering theory

We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists for arbitrary dilated spatial regions symmetric with respect to the origin. It is equal to the usual time delay plus a new contribution, which vanishes in the case of spherical spatial regions. We also prove that the symmetrized time delay is invariant under an appropriate mapping of time reversal. These results are also discussed in the context of classical scattering theory.Comment: 18 page

Remarks on Resonant Scalars in the AdS/CFT Correspondence

The special properties of scalars having a mass such that the two possible dimensions of the dual scalar respect the unitarity and the Breitenlohner-Freedman bounds and their ratio is integral (``resonant scalars'') are studied in the AdS/CFT correspondence. The role of logarithmic branches in the gravity theory is related to the existence of a trace anomaly and to a marginal deformation in the Conformal Field Theory. The existence of asymptotic charges for the conformal group in the gravity theory is interpreted in terms of the properties of the corresponding CFT.Comment: 16 pages, 1 figur

New Results on Holographic Three-Point Functions

We exploit a gauge invariant approach for the analysis of the equations governing the dynamics of active scalar fluctuations coupled to the fluctuations of the metric along holographic RG flows. In the present approach, a second order ODE for the active scalar emerges rather simply and makes it possible to use the Green's function method to deal with (quadratic) interaction terms. We thus fill a gap for active scalar operators, whose three-point functions have been inaccessible so far, and derive a general, explicitly Bose symmetric formula thereof. As an application we compute the relevant three-point function along the GPPZ flow and extract the irreducible trilinear couplings of the corresponding superglueballs by amputating the external legs on-shell.Comment: v2: reference added, typos corrected v3: sign convention for background changed, agrees with version published in JHE

Universal Features of Holographic Anomalies

We study the mechanism by which gravitational actions reproduce the trace anomalies of the holographically related conformal field theories. Two universal features emerge: a) the ratios of type B trace anomalies in any even dimension are independent of the gravitational action, being uniquely determined by the underlying algebraic structure b) the normalization of the type A and the overall normalization of the type B anomalies are given by action dependent expressions with the dimension dependence completely fixed.Comment: 17 pages, harvma

Chandra observations of the planetary nebula IC 4593

The ACIS-S camera on board the Chandra X-ray Observatory has been used to discover a hot bubble in the planetary nebula (PN) IC4593, the most distant PN detected by Chandra so far. The data are used to study the distribution of the X-ray-emitting gas in IC 4593 and to estimate its physical properties. The hot bubble has a radius of ~2$^{\prime\prime}$ and is found to be confined inside the optically-bright innermost cavity of IC 4593. The X-ray emission is mostly consistent with that of an optically-thin plasma with temperature $kT\approx0.15$ keV (or $T_\mathrm{X}\approx1.7\times10^{6}$ K), electron density $n_\mathrm{e}\approx15$ cm$^{-3}$, and intrinsic X-ray luminosity in the 0.3-1.5 keV energy range $L_\mathrm{X}=3.4\times10^{30}$ erg s$^{-1}$. A careful analysis of the distribution of hard ($E>$0.8 keV) photons in IC 4593 suggests the presence of X-ray emission from a point source likely associated with its central star (CSPN). If this were the case, its estimated X-ray luminosity would be $L_\mathrm{X,CSPN}=7\times10^{29}$ erg s$^{-1}$, fulfilling the log$(L_\mathrm{X,CSPN}/L_\mathrm{bol})\approx-7$ relation for self-shocking winds in hot stars. The X-ray detection of the CSPN helps explain the presence of high-ionisation species detected in the UV spectra as predicted by stellar atmosphere models.Comment: 6 pages, 4 figures; Accepted to MNRA

Extreme Warm Absorber variability in the Seyfert Galaxy Mrk 704

In about half of Seyfert galaxies, the X-ray emission is absorbed by an optically thin, ionized medium, the so-called "Warm Absorber", whose origin and location is still a matter of debate. The aims of this paper is to put more constraints on the warm absorber by studying its variability. We analyzed the X-ray spectra of a Seyfert 1 galaxy, Mrk 704, which was observed twice, three years apart, by XMM-Newton. The spectra were well fitted with a two zones absorber, possibly covering only partially the source. The parameters of the absorbing matter - column density, ionization state, covering factor - changed significantly between the two observations. Possible explanations for the more ionized absorber are a torus wind (the source is a polar scattering one) or, in the partial covering scenario, an accretion disk wind. The less ionized absorber may be composed of orbiting clouds in the surroundings of the nucleus, similarly to what already found in other sources, most notably NGC 1365.Comment: 10 pages. Accepted for publication in Astronomy & Astrophysic

Transmission resonances and supercritical states in a one dimensional cusp potential

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.Comment: 10 pages. Revtex 4. To appear in Phys Rev.

Time delay for one-dimensional quantum systems with steplike potentials

This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"{o}dinger Hamiltonian $H = -\Delta + V$ with a potential $V(x)$ converging to different limits $V_{\ell}$ and $V_{r}$ as $x \to -\infty$ and $x \to +\infty$ respectively. Due to the anisotropy they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V(x)$ vanishes as $|x| \to \infty$ ($V_\ell = V_r$). We show that it remains true in the anisotropic case $V_\ell \not = V_r$, i.e. we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression which is commonly used for time delay in the literature.Comment: 48 pages, 1 figur