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.

Mode Fluctuation Distribution for Spectra of Superconducting Microwave Billiards

High resolution eigenvalue spectra of several two- and three-dimensional superconducting microwave cavities have been measured in the frequency range below 20 GHz and analyzed using a statistical measure which is given by the distribution of the normalized mode fluctuations. For chaotic systems the limit distribution is conjectured to show a universal Gaussian, whereas integrable systems should exhibit a non-Gaussian limit distribution. For the investigated Bunimovich stadium and the 3D-Sinai billiard we find that the distribution is in good agreement with this prediction. We study members of the family of limacon billiards, having mixed dynamics. It turns out that in this case the number of approximately 1000 eigenvalues for each billiard does not allow to observe significant deviations from a Gaussian, whereas an also measured circular billiard with regular dynamics shows the expected difference from a Gaussian.Comment: 7 pages, RevTex, 5 postscript figure, to be published in Phys. Rev. E. In case of any problems contact A. Baecker ([email protected]) or H. Rehfeld ([email protected]

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.

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]

Coupled Microwave Billiards as a Model for Symmetry Breaking

Two superconducting microwave billiards have been electromagnetically coupled in a variable way. The spectrum of the entire system has been measured and the spectral statistics analyzed as a function of the coupling strength. It is shown that the results can be understood in terms of a random matrix model of quantum mechanical symmetry breaking -- as e.g. the violation of parity or isospin in nuclear physics.Comment: 4 pages, 5 figure

First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard

We report on first experimental signatures for chaos-assisted tunneling in a two-dimensional annular billiard. Measurements of microwave spectra from a superconducting cavity with high frequency resolution are combined with electromagnetic field distributions experimentally determined from a normal conducting twin cavity with high spatial resolution to resolve eigenmodes with properly identified quantum numbers. Distributions of so-called quasi-doublet splittings serve as basic observables for the tunneling between whispering gallery type modes localized to congruent, but distinct tori which are coupled weakly to irregular eigenstates associated with the chaotic region in phase space.Comment: 5 pages RevTex, 5 low-resolution figures (high-resolution figures: http://linac.ikp.physik.tu-darmstadt.de/heiko/chaospub.html, to be published in Phys. Rev. Let

Investigation of the long-term sustainability of changes in appetite after weight loss

Background/Objective Diet-induced weight loss (WL) leads to a compensatory increase in appetite and changes in the plasma concentration of appetite-regulating hormones are likely to play a role. Whether these changes are transient or sustained remains unclear. This study aimed to assess if changes in subjective and objective appetite markers observed with WL are sustained after 1 year (1Y).Subjects/Methods In total 100 (45 males) individuals with obesity (BMI: 37 +/- 4 kg/m(2), age: 43 +/- 10 years) underwent 8 weeks (wks) of a very-low energy diet (VLED), followed by 4 wks refeeding, and a 1Y maintenance program. Fasting/postprandial subjective ratings of hunger, fullness, desire to eat, and prospective food consumption (PFC) were assessed, and plasma concentration of active ghrelin (AG), total peptide YY (PYY), active glucagon-like peptide 1, cholecystokinin (CCK), and insulin measured, at baseline, week 13 (Wk13) and 1Y.Results At Wk13, 16% WL (-18 +/- 1 kg, P < 0.001) was associated with a significant increase in fasting and postprandial hunger ratings (P < 0.01 and P < 0.05, respectively), and postprandial fullness (P < 0.01) combined with a reduction in PFC (P < 0.001). These were accompanied by a significant rise in basal and postprandial AG concentrations (P < 0.001, for both), a reduction in postprandial CCK (P < 0.01) and in basal and postprandial insulin (P < 0.001). At 1Y follow-up, with sustained WL (15%; -16 +/- 1 kg, P < 0.001), fasting hunger and postprandial fullness ratings remained increased (P < 0.05 for both), and postprandial PFC reduced (P < 0.001). Basal and postprandial AG remained elevated and insulin reduced (P < 0.001, for all), while postprandial CCK was increased (P < 0.01) and PYY decreased (P < 0.001).Conclusion With a 15% sustained WL at 1Y, the drive to eat in the fasting state is increased, but this may be balanced out by raised postprandial feelings of fullness. To assist with WL maintenance, new strategies are required to manage increased hunger and drive to eat