A quantum graph approach to metamaterial design.

Since the turn of the century, metamaterials have gained a large amount of attention due to their potential for possessing highly nontrivial and exotic properties-such as cloaking or perfect lensing. There has been a great push to create reliable mathematical models that accurately describe the required material composition. Here, we consider a quantum graph approach to metamaterial design.

A wave finite element approach for modelling wave transmission through laminated plate junctions.

We present a numerical method for computing reflection and transmission coefficients at joints connecting composite laminated plates. The method is based on modelling joints with finite elements with boundary conditions given by the solutions of the wave finite element method for the plates in the infinite half-spaces connected to the joint. There are no restrictions on the number of plates, inter-plate angles, and material parameters of individual layers forming the composite.

Wireless power distributions in multi-cavity systems at high frequencies.

The next generations of wireless networks will work in frequency bands ranging from sub-6 GHz up to 100 GHz. Radio signal propagation differs here in several critical aspects from the behaviour in the microwave frequencies currently used. With wavelengths in the millimetre range (mmWave), both penetration loss and free-space path loss increase, while specular reflection will dominate over diffraction as an important propagation channel.

Stochastic electromagnetic field propagation- measurement and modelling.

This paper reviews recent progress in the measurement and modelling of stochastic electromagnetic fields, focusing on propagation approaches based on Wigner functions and the method of moments technique. The respective propagation methods are exemplified by application to measurements of electromagnetic emissions from a stirred, cavity-backed aperture. We discuss early elements of statistical electromagnetics in Heaviside's papers, driven mainly by an analogy of electromagnetic wave propagation with heat transfer.

Microwave experiments simulating quantum search and directed transport in artificial graphene.

A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to √N, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover's original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points.

A boundary integral formalism for stochastic ray tracing in billiards.

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty.

Quantum search on graphene lattices.

We present a continuous-time quantum search algorithm on a graphene lattice. This provides the sought-after implementation of an efficient continuous-time quantum search on a two-dimensional lattice. The search uses the linearity of the dispersion relation near the Dirac point and can find a marked site on a graphene lattice faster than the corresponding classical search.

Subdeterminant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs.

We study the implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into subdeterminants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple subdeterminant identity which has a nontrivial interpretation in terms of pseudo-orbits.

A hybrid approach for predicting the distribution of vibro-acoustic energy in complex built-up structures.

Finding the distribution of vibro-acoustic energy in complex built-up structures in the mid-to-high frequency regime is a difficult task. In particular, structures with large variation of local wavelengths and/or characteristic scales pose a challenge referred to as the mid-frequency problem. Standard numerical methods such as the finite element method (FEM) scale with the local wavelength and quickly become too large even for modern computer architectures.

Wave communication across regular lattices.

We propose a novel way to communicate signals in the form of waves across a d-dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to communicate between two (or more) points on the lattice. Remarkably, neither the sender nor the receiver needs to know the position of each other despite the fact that the signal is only exchanged between the contributing parties.

Scaling laws for the photoionization cross section of two-electron atoms.

The cross sections for single-electron photoionization in two-electron atoms show fluctuations which decrease in amplitude when approaching the double-ionization threshold. Based on semiclassical closed orbit theory, we show that the algebraic decay of the fluctuations can be characterized in terms of a threshold law sigma proportional to |E|(mu) as E --> 0(-) with exponent mu obtained as a combination of stability exponents of the triple-collision singularity. It differs from Wannier's exponent dominating double-ionization processes.

Short wavelength approximation of a boundary integral operator for homogeneous and isotropic elastic bodies.

A short wavelength approximation of a boundary integral operator for two-dimensional isotropic and homogeneous elastic bodies is derived from first principles starting from the Navier-Cauchy equation. Trace formulas for elastodynamics are deduced connecting the eigenfrequency spectrum of an elastic body to the set of periodic rays where mode conversion enters as a dynamical feature.

Classical dynamics of two-electron atoms at zero energy.

We give a complete description of the classical dynamics of two electrons in the Coulomb potential of a positively charged nucleus for total energy E=0 and angular momentum L=0. The effectively four-dimensional phase space can be divided into partitions spanned by the stable and unstable manifold of the Wannier ridge space. We identify a further approximate symmetry by choosing an appropriate Poincaré surface of section in this dynamical system.

Classical dynamics of two-electron atoms near the triple collision.

The classical dynamics of two electrons in the Coulomb potential of an attractive nucleus is chaotic in large parts of the high-dimensional phase space. Quantum spectra of two-electron atoms, however, exhibit structures which clearly hint at the existence of approximate symmetries in this system. In a recent paper [Phys.

Classical dynamics near the triple collision in a three-body Coulomb problem.

We investigate the classical motion of three charged particles with both attractive and repulsive interactions. The triple collision is a main source of chaos in such three-body Coulomb problems. By employing the McGehee scaling technique, we analyze here for the first time in detail the three-body dynamics near the triple collision in 3 degrees of freedom.

Wave chaos in the elastic disk.

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics.

Quantization of chaotic systems.

Starting from the semiclassical dynamical zeta function for chaotic Hamiltonian systems we use a combination of the cycle expansion method and a functional equation to obtain highly excited semiclassical eigenvalues. The power of this method is demonstrated for the anisotropic Kepler problem, a strongly chaotic system with good symbolic dynamics. An application of the transfer matrix approach of Bogomolny is presented leading to a significant reduction of the classical input and to comparable accuracy for the calculated eigenvalues.