1,192 research outputs found
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 with . 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
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