Typical length scales in conducting disorderless networks

We take advantage of a recently established equivalence, between the intermittent dynamics of a deterministic nonlinear map and the scattering matrix properties of a disorderless double Cayley tree lattice of connectivity $K$, to obtain general electronic transport expressions and expand our knowledge of the scattering properties at the mobility edge. From this we provide a physical interpretation of the generalized localization length.Comment: 12 pages, 3 figure

Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices

The problem of chaotic scattering in presence of direct processes or prompt responses is mapped via a transformation to the case of scattering in absence of such processes for non-unitary scattering matrices, \tilde S. In the absence of prompt responses, \tilde S is uniformly distributed according to its invariant measure in the space of \tilde S matrices with zero average, < \tilde S > =0. In the presence of direct processes, the distribution of \tilde S is non-uniform and it is characterized by the average (\neq 0). In contrast to the case of unitary matrices S, where the invariant measures of S for chaotic scattering with and without direct processes are related through the well known Poisson kernel, here we show that for non-unitary scattering matrices the invariant measures are related by the Poisson kernel squared. Our results are relevant to situations where flux conservation is not satisfied. For example, transport experiments in chaotic systems, where gains or losses are present, like microwave chaotic cavities or graphs, and acoustic or elastic resonators.Comment: Added two appendices and references. Corrected typo

Experimental determination of the absorption strength in absorbing chaotic cavities

Due to the experimental necessity we present a formula to determine the absorption strength by power losses inside a chaotic system (cavities, graphs, acoustic resonators, etc) when the antenna coupling, always present in experimental measurements, is taken into account. This is done by calculating the average of the absorption coefficient as a function of the absorption strength and the coupling of the antenna to the system, in the one channel case.Comment: 6 pages, 3 figures, Submitted to Phys. Rev.

Geant4 Monte Carlo simulation study of the secondary radiation fields at the laser-driven ion source LION

At the Center for Advanced Laser Applications (CALA), Garching, Germany, the LION (Laser-driven ION Acceleration) experiment is being commissioned, aiming at the production of laser-driven bunches of protons and light ions with multi-MeV energies and repetition frequency up to 1 Hz. A Geant4 Monte Carlo-based study of the secondary neutron and photon fields expected during LION’s different commissioning phases is presented. Goal of this study is the characterization of the secondary radiation environment present inside and outside the LION cave. Three different primary proton spectra, taken from experimental results reported in the literature and representative of three different future stages of the LION’s commissioning path are used. Together with protons, also electrons are emitted through laser-target interaction and are also responsible for the production of secondary radiation. For the electron component of the three source terms, a simplified exponential model is used. Moreover, in order to reduce the simulation complexity, a two-components simplified geometrical model of proton and electron sources is proposed. It has been found that the radiation environment inside the experimental cave is either dominated by photons or neutrons depending on the position in the room and the source term used. The higher the intensity of the source, the higher the neutron contribution to the total dose for all scored positions. Maximum neutron and photon ambient dose equivalent values normalized to 10(9) simulated incident primaries were calculated at the exit of the vacuum chamber, where values of about 85 nSv (10(9) primaries)(−1) and 1.0 μSv (10(9) primaries)(−1) were found

Poynting's theorem for planes waves at an interface: a scattering matrix approach

We apply the Poynting theorem to the scattering of monochromatic electromagnetic planes waves with normal incidence to the interface of two different media. We write this energy conservation theorem to introduce a natural definition of the scattering matrix S. For the dielectric-dielectric interface the balance equation lead us to the energy flux conservation which express one of the properties of S: it is a unitary matrix. For the dielectric-conductor interface the scattering matrix is no longer unitary due to the presence of losses at the conductor. However, the dissipative term appearing in the Poynting theorem can be interpreted as a single absorbing mode at the conductor such that a whole S, satisfying flux conservation and containing this absorbing mode, can be defined. This is a simplest version of a model introduced in the current literature to describe losses in more complex systems.Comment: 5 pages, 3 figures, submitted to Am. J. Phy