Relation between phase and dwell times for quantum tunneling of a relativistically propagating particle

The general and explicit relation between the phase time and the dwell time for quantum tunneling of a relativistically propagating particle is investigated and quantified. In analogy with previously obtained non-relativistic results, it is shown that the group delay can be described in terms of the dwell time and a self-interference delay. Lessons concerning the phenomenology of the relativistic tunneling are drawn

On the average Gamma-Ray Burst X-ray flaring activity

Gamma-ray burst X-ray flares are believed to mark the late time activity of the central engine. We compute the temporal evolution of the average flare luminosity $$ in the common rest frame energy band of 44 GRBs taken from the large \emph{Swift} 5-years data base. Our work highlights the importance of a proper consideration of the threshold of detection of flares against the contemporaneous continuous X-ray emission. In the time interval $30 \rm{s}\propto t^{-2.7\pm 0.1}$; this implies that the flare isotropic energy scaling is $E_{\rm{iso,flare}}\propto t^{-1.7}$. The decay of the continuum underlying the flare emission closely tracks the average flare luminosity evolution, with a typical flare to steep-decay luminosity ratio which is $L_{\rm{flare}}/L_{\rm{steep}}=4.7$: this suggests that flares and continuum emission are deeply related to one another. We infer on the progenitor properties considering different models. According to the hyper-accreting black hole scenario, the average flare luminosity scaling can be obtained in the case of rapid accretion ($t_{\rm{acc}}\ll t$) or when the last \sim 0.5 M_{\sun} of the original 14 M_{\sun} progenitor star are accreted. Alternatively, the steep $\propto t^{-2.7}$ behaviour could be triggered by a rapid outward expansion of an accretion shock in the material feeding a convective disk. If instead we assume the engine to be a rapidly spinning magnetar, then its rotational energy can be extracted to power a jet whose luminosity is likely to be between the monopole ($L\propto e^{-2t}$) and dipole ($L\propto t^{-2}$) cases. In both scenarios we suggest the variability, which is the main signature of the flaring activity, to be established as a consequence of different kinds of instabilities.Comment: MNRAS accepte

Conditional entropy of glueball states

The conditional entropy of glueball states is calculated using a holographic description. Glueball states are represented by a supergravity dual picture, consisting of a 5-dimensional graviton-dilaton action of a dynamical holographic AdS/QCD model. The conditional entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.Comment: 6 pages, 4 figure

The X-ray light curve of Gamma-ray bursts: clues to the central engine

We present the analysis of a large sample of gamma-ray burst (GRB) X-ray light curves in the rest frame to characterise their intrinsic properties in the context of different theoretical scenarios. We determine the morphology, time scales, and energetics of 64 long GRBs observed by \emph{Swift}/XRT \emph{without} flaring activity. We furthermore provide a one-to-one comparison to the properties of GRBs \emph{with} X-ray flares. We find that the steep decay morphology and its connection with X-ray flares favour a scenario in which a central engine origin. We show that this scenario can also account for the shallow decay phase, provided that the GRB progenitor star has a self-similar structure with a constant envelope-to-core mass ratio $\sim 0.02-0.03$. However, difficulties arise for very long duration ($t_p\gtrsim10^4$ s) shallow phases. Alternatively, a spinning-down magnetar whose emitted power refreshes the forward shock can quantitatively account for the shallow decay properties. In particular we demonstrate that this model can account for the plateau luminosity vs. end time anticorrelation.Comment: 12 pages, 8 figures, accepted for publication in A&