Experimental vs. Numerical Eigenvalues of a Bunimovich Stadium Billiard -- A Comparison

We compare the statistical properties of eigenvalue sequences for a gamma=1 Bunimovich stadium billiard. The eigenvalues have been obtained by two ways: one set results from a measurement of the eigenfrequencies of a superconducting microwave resonator (real system) and the other set is calculated numerically (ideal system). The influence of the mechanical imperfections of the real system in the analysis of the spectral fluctuations and in the length spectra compared to the exact data of the ideal system are shown. We also discuss the influence of a family of marginally stable orbits, the bouncing ball orbits, in two microwave stadium billiards with different geometrical dimensions.Comment: RevTex, 8 pages, 8 figures (postscript), to be published in Phys. Rev.

Global attractivity of the equilibrium of a nonlinear difference equation

summary:The authors consider the nonlinear difference equation $$x_{n+1}=\alpha x_n + x_{n-k}f(x_{n-k}), \quad n=0, 1,\dots .1 \text{where} \alpha \in (0, 1),\hspace{5.0pt}k \in \lbrace 0, 1, \dots \rbrace \hspace{5.0pt}\text{and}\hspace{5.0pt}f\in C^1[[0, \infty ),[0, \infty )] \qquad \mathrm{(0)}$$ with $f^{\prime }(x)<0$. They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given

Anderson Localization in a String of Microwave Cavities

The field distributions and eigenfrequencies of a microwave resonator which is composed of 20 identical cells have been measured. With external screws the periodicity of the cavity can be perturbed arbitrarily. If the perturbation is increased a transition from extended to localized field distributions is observed. For very large perturbations the field distributions show signatures of Anderson localization, while for smaller perturbations the field distribution is extended or weakly localized. The localization length of a strongly localized field distribution can be varied by adjusting the penetration depth of the screws. Shifts in the frequency spectrum of the resonator provide further evidence for Anderson localization.Comment: 7 pages RevTex, to be published in Phys. Rev.

Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states

We examine the propagation of the recently-discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions, stationary Landau states manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the non-rotating superpositions reproduce stable multi-vortex configurations that appear in rotating superfluids. Our results open up an avenue for the direct electron-microscopy observation of fundamental properties of free quantum electron states in magnetic fields.Comment: 21 pages, 10 figures, 1 table, to appear in Phys. Rev.

Wave Dynamical Chaos in a Superconducting Three-Dimensional Sinai Billiard

Based on very accurate measurements performed on a superconducting microwave resonator shaped like a desymmetrized three-dimensional (3D) Sinai billiard, we investigate for the first time spectral properties of the vectorial Helmholtz, i.e. non-quantum wave equation for a classically totally chaotic and theoretically precisely studied system. We are thereby able to generalize some aspects of quantum chaos and present some results which are consequences of the polarization features of the electromagnetic waves.Comment: 4 pages RevTex; 4 postscript figures; to be published in Phys. Rev. Lett.; Info: [email protected]

The role of Dark Matter interaction in galaxy clusters

We consider a toy model to analyze the consequences of dark matter interaction with a dark energy background on the overall rotation of galaxy clusters and the misalignment between their dark matter and baryon distributions when compared to {\Lambda}CDM predictions. The interaction parameters are found via a genetic algorithm search. The results obtained suggest that interaction is a basic phenomenon whose effects are detectable even in simple models of galactic dynamics.Comment: RevTeX 4.1, 5 pages, 3 figure