Hadronic models of blazars require a change of the accretion paradigm

We study hadronic models of broad-band emission of jets in radio-loud active galactic nuclei, and their implications for the accretion in those sources. We show that the models that account for broad-band spectra of blazars emitting in the GeV range in the sample of Boettcher et al. have highly super-Eddington jet powers. Furthermore, the ratio of the jet power to the radiative luminosity of the accretion disc is $\sim 3000$ on average and can be as high as $\sim 10^5$. We then show that the measurements of the radio core shift for the sample imply low magnetic fluxes threading the black hole, which rules out the Blandford-Znajek mechanism to produce powerful jets. These results require that the accretion rate necessary to power the modelled jets is extremely high, and the average radiative accretion efficiency is $\sim 4 \times 10^{-5}$. Thus, if the hadronic model is correct, the currently prevailing picture of accretion in AGNs needs to be significantly revised. Also, the obtained accretion mode cannot be dominant during the lifetimes of the sources, as the modelled very high accretion rates would result in too rapid growth of the central supermassive black holes. Finally, the extreme jet powers in the hadronic model are in conflict with the estimates of the jet power by other methods.Comment: MNRAS, in pres

The Spectra of Large Toeplitz Band Matrices with a Randomly Perturbed Entry

This report is concerned with the union $sp_{\Omega}^{(j,k)}T_{n}(a)$ of all possible spectra that may emerge when perturbing a large $n \times n$ Toeplitz band matrix $T_{n}(a)$ in the $(j,k)$ site by a number randomly chosen from some set $\Omega$. The main results give descriptive bounds and, in several interesting situations, even provide complete identifications of the limit of $sp_{\Omega}^{(j,k)}T_{n}(a)$ as $n \to \infty$. Also discussed are the cases of small and large sets $\Omega$ as well as the "discontinuity of the infinite volume case", which means that in general $sp_{\Omega}^{(j,k)}T_{n}(a)$ does not converge to something close to $sp_{\Omega}^{(j,k)}T_{n}(a)$ as $n \to \infty$, where $T(a)$ is the corresponding infinite Toeplitz matrix. Illustrations are provided for tridiagonal Toeplitz matrices, a notable special case. \ud \ud The second author was supported by UK Enginering and Physical Sciences Research Council Grant GR/M1241

Quantum Transport through Hierarchical Structures

The transport of quantum electrons through hierarchical lattices is of interest because such lattices have some properties of both regular lattices and random systems. We calculate the electron transmission as a function of energy in the tight binding approximation for two related Hanoi networks. HN3 is a Hanoi network with every site having three bonds. HN5 has additional bonds added to HN3 to make the average number of bonds per site equal to five. We present a renormalization group approach to solve the matrix equation involved in this quantum transport calculation. We observe band gaps in HN3, while no such band gaps are observed in linear networks or in HN5.Comment: 15 pages, RevTex, 10 figures, for related work, see http://www.physics.emory.edu/faculty/boettcher

Moments of Coinless Quantum Walks on Lattices

The properties of the coinless quantum walk model have not been as thoroughly analyzed as those of the coined model. Both evolve in discrete time steps but the former uses a smaller Hilbert space, which is spanned merely by the site basis. Besides, the evolution operator can be obtained using a process of lattice tessellation, which is very appealing. The moments of the probability distribution play an important role in the context of quantum walks. The ballistic behavior of the mean square displacement indicates that quantum-walk-based algorithms are faster than random-walk-based ones. In this paper, we obtain analytical expressions for the moments of the coinless model on $d$-dimensional lattices. The mean square displacement for large times is explicitly calculated for the one- and two-dimensional lattices and, using optimization methods, the parameter values that give the largest spread are calculated and compared with the equivalent ones of the coined model. Although we have employed asymptotic methods, our approximations are accurate even for small numbers of time steps.Comment: 13 pages, 1 figur