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The signatures of wave functions in open cylindrical microwave billiards are investigated. The wave functions are obtained by means of a transmission measurement from an attached lead to a probe antenna inside the billiard. One can deduce complex wave functions and current densities of the system from the measurement. We investigate distributions and correlations of wave functions, currents and other quantities and compare this results with predictions from the random plane wave approach. Vortices and saddles are created and annihilated as a function of frequency and show a rich dynamic. Additionally we investigate nodal domains of the real and imaginary part of the wave function, their relation to the phase rigidity, and its parametric dependance on global phase shifts.

Abstract.: The signatures of wave functions in open cylindrical microwave billiards are investigated. The wave functions are obtained by means of a transmission measurement from an attached lead to a probe antenna inside the billiard. One can deduce complex wave functions and current densities of the system from the measurement. We investigate distributions and correlations of wave functions, currents and other quantities and compare this results with predictions from the random plane wave approach. Vortices and saddles are created and annihilated as a function of frequency and show a rich dynamic. Additionally we investigate nodal domains of the real and imaginary part of the wave function, their relation to the phase rigidity, and its parametric dependance on global phase shifts.

Experimental results on spectra and wave functions of a ray-splitting microwave billiard are presented. The billiard is formed by a flat rectangular microwave cavity with a quarter-circle insert made of teflon in one of the corners. Using the Gutzwiller trace formula, the contribution of the periodic orbits of the billiard to the density of states are determined. The wave functions, many of them showing scars associated with periodic orbits, are interpreted in terms of the semiclassical Green function.

3,7-Diazabicyclo[3.3.1]nonan-9-ones having aryl rings in positions 2 and 4 with systematically varied substituents were synthesized using a double Mannich procedure. Radioligand binding assays were performed to measure the affinity of the compounds to the μ-, δ-, and κ-opioid receptors. The affinity of all 2,4-diphenyl-substituted 3,7-diazabicyclo[3.3.1]nonan-9-ones to the μ- and δ-receptors was found to be low. In contrast, with exception of the nitro- and cyanophenyl-substituted compounds, most of the diazabicycles showed considerable affinity for the κ-receptor. In particular, the m-fluoro-, p-methoxy-, and m-hydroxy-substituted compounds have an affinity in the submicromolar range. Due to solubility problems in aqueous media, salts of HZ2 were synthesized. The methiodide shows high κ-affinity and may, thus, be a promising candidate for development of a peripheral κ-agonist, e.g. for use in the case of rheumatoid arthritis.

Abstract:: A set-up is described allowing the automatic registration of wavefunctions of quasi-two-dimensional microwave billiards of arbitrary shape. Tests of the apparatus with rectangular shaped billiards showed that a precision of some percent in the wavefunction amplitudes can be obtained, as far as isolated resonances are considered. For the case of overlapping resonances, however, the measurement yields wavefunctions which are close to a symmetric and an antisymmetric linear combination of the original rectangle eigenfunctions. The cause for this at first sight surprising result is discussed.

We measure the angular momentum content of modes in a flat, near-circular microwave cavity with a rough perimeter and demonstrate localization in angular momentum space. Because Schrödinger's wave mechanics and Maxwell's electrodynamics are equivalent for a 2d cavity, we compare our experimental results directly with the quantum theory of rough 2d cavities [K.M. Frahm and D.L. Shepelyansky, Phys. Rev. Lett. 78 (1997) 1440]. Introducing the concept of effective roughnesswe find good qualitative agreement.

The spectra of Sinai microwave billiards and rectangular billiards with statistically distributed circular scatterers have been taken as a function of the position of one wall, and of one of the scatterers, respectively. Whereas in the first case the velocity distribution and correlations obey the universal behaviour predicted by Simons and Altshuler, in the second case a completely different behaviour is observed. This is due to the fact that a shift of one wall changes the wave function globally whereas the displacement of one scatterer only leads to a local perturbance.

Postprandial renal blood flow was studied in 14 conscious dogs on a chronic high and low sodium intake on 72 days after implantation of an electromagnetic flow transducer around the left renal artery. Fasting renal blood flow was 11.7±3.2 ml/min·kg on high sodium intake (43 days) and 11.5±3.3 ml/min·kg on low sodium intake (29 days). During ingestion no change of renal blood flow occurred; mean arterial pressure rose transiently. During digestion renal blood flow increased always and was, like the fasting renal blood flow, independent of the daily sodium intake: maximum increase of renal blood flow of dogs on a high sodium intake was 41±23%, and of dogs on a low sodium intake 35±155 referring to fasting controls; peak increase mostly occurred between 60 and 90 min postprandially and was due to a decrease of renal vascular resistance.

Conscious dogs were used to study whether changes in total renal hemodynamics are responsible for diuresis and natriuresis during an experimental increase in left atrial pressure (LAP). To ensure a controlled dietary sodium intake, the dogs (n=8) were chronically kept on ahigh or alow sodium intake diet (HSI; LSI). After the dogs had completely recovered from surgery (carotid loop, thoracotomy, flank incision), LAP was increased by about 10 cm H2O for 60 min by tightening a purse string around the mitral annulus (51 expts). Mean urine volume (V) increased in both groups to a comparable degree. Mean sodium excretion increased somewhat more in HSI dogs, but remained elevated in LSI dogs after the LAP increase. Renal blood flow (electromagnetic flow transducer) and inulin clearance did not change. Renal vascular resistance (RVR) increased by about 20% (HSI) and 15% (LSI). — When the induced LAP increase was terminated, V decreased. RVR decreased in HSI dogs by about -11% and in LSI dogs by about -6% below control values.—It is concluded that volume regulatory mechanisms induced by an experimental LAP increase operate independently of changes in total renal blood flow.

10 conscious chronically prepared dogs were used. After recovery from thoracotomy (catheter into the left atrium, nylon purse string around the mitral annulus) they were kept chronically on a low sodium intake (<0.5 meq Na/kg bw daily). On 51 days left atrial pressure (LAP) was increased for 60 min about 10 cm H2O once daily by tightening the purse string (distension period: DP).

Summary 5 conscious, well trained, female dogs kept on a high sodium intake (14 meq Na/kg bw) were used to measureeft atrial pressure (LAP), urine volume ( $$\dot V$$ ), sodium and potassium excretion (UNa $$\dot V$$ , UK $$\dot V$$ ) as well as plasma osmolality (Posm) before and up to 180 minafter food intake. The dogs were fitted with a catheter in the left atrium (thoracotomy). In all experiments (n=23) LAP increased postprandially (pp) above fasting controls. The mean peak increase range from 4 to 6 cm H2O and was observed as early as 61–80 and as late, as 161–180 min pp. Increase in LAP was closely correlated to V which rose from 36±28 to 160±51 ul/min·kg. pp $$\dot V$$ was also correlated to pp UNa $$\dot V$$ which increased from 4.8±3.3 to 34.0±8.5 ueq/min·kg.

Using the equivalence between the quantum-mechanical probability density in a quantum billiard and the Poynting vector in the corresponding microwave system, current distributions were studied in a quantum dot like cavity, as well as in a Robnik billiard with λ=0.4, and an introduced ferrite cylinder. Spatial auto correlation functions for currents and vorticity were studied and compared with predictions from the random-superposition-of-plane-waves hypothesis. In addition different types of vortex neighbour spacing distributions were determined and compared with theory.