On the Role of Non-Periodic Orbits in The Semiclassical Quantization of the Truncated Hyperbola Billiard

Based on an accurate computation of the first 1851 quantal energy levels of the truncated hyperbola billiard, we have found an anomalous long-range modulation in the integrated level density. It is shown that the observed anomaly can be explained by an additional term in Gutzwiller's trace formula. This term is given as a sum over families of closed, non-periodic orbits which are reflected in a point of the billiard boundary where the boundary is continuously differentiable, but its curvature radius changes discontinuously.Comment: 8 pages, uu-encoded ps-fil

Mode fluctuations as fingerprint of chaotic and non-chaotic systems

The mode-fluctuation distribution $P(W)$ is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the $E(k,L)$ functions being the probability of finding $k$ energy levels in a randomly chosen interval of length $L$, and the distribution of $n(L)$, where $n(L)$ is the number of levels in such an interval, and their cumulants $c_k(L)$. It is demonstrated that the cumulants provide a possible measure for the distinction between chaotic and non-chaotic systems. The vanishing of the normalized cumulants $C_k$, $k\geq 3$, implies a Gaussian behaviour of $P(W)$, which is realized in the case of chaotic systems, whereas non-chaotic systems display non-vanishing values for these cumulants leading to a non-Gaussian behaviour of $P(W)$. For some integrable systems there exist rigorous proofs of the non-Gaussian behaviour which are also discussed. Our numerical results and the rigorous results for integrable systems suggest that a clear fingerprint of chaotic systems is provided by a Gaussian distribution of the mode-fluctuation distribution $P(W)$.Comment: 44 pages, Postscript. The figures are included in low resolution only. A full version is available at http://www.physik.uni-ulm.de/theo/qc/baecker.htm

Numerical computation of Maass waveforms and an application to cosmology

We compute numerically eigenvalues and eigenfunctions of the Laplacian in a three-dimensional hyperbolic space. Applying the results to cosmology, we demonstrate that the methods learned in quantum chaos can be used in other fields of research.Comment: A version of the paper with high resolution figures is available at http://www.physik.uni-ulm.de/theo/qc/publications.htm

Energy-dependent evolution in IC10 X-1: hard evidence for an extended corona and implications

We have analyzed a ~130 ks XMM-Newton observation of the dynamically confirmed black hole + Wolf-Rayet (BH+WR) X-ray binary (XB) IC10 X-1, covering ~1 orbital cycle. This system experiences periodic intensity dips every ~35 hr. We find that energy-independent evolution is rejected at a >5σ level. The spectral and timing evolution of IC10 X-1 are best explained by a compact disk blackbody and an extended Comptonized component, where the thermal component is completely absorbed and the Comptonized component is partially covered during the dip. We consider three possibilities for the absorber: cold material in the outer accretion disk, as is well documented for Galactic neutron star (NS) XBs at high inclination; a stream of stellar wind that is enhanced by traveling through the L1 point; and a spherical wind. We estimated the corona radius (r ADC) for IC10 X-1 from the dip ingress to be ~106 km, assuming absorption from the outer disk, and found it to be consistent with the relation between r ADC and 1-30 keV luminosity observed in Galactic NS XBs that spans two orders of magnitude. For the other two scenarios, the corona would be larger. Prior BH mass (M BH) estimates range over 23-38 M ☉, depending on the inclination and WR mass. For disk absorption, the inclination, i, is likely to be ~60-80°, with M BH ~ 24-41 M ☉. Alternatively, the L1-enhanced wind requires i ~ 80°, suggesting ~24-33 M ☉. For a spherical absorber, i ~ 40°, and M BH ~ 50-65 M ☉

A Parallax Distance to the Microquasar GRS 1915+105 and a Revised Estimate of its Black Hole Mass

Using the Very Long Baseline Array, we have measured a trigonometric parallax for the micro quasar GRS 1915+105, which contains a black hole and a K-giant companion. This yields a direct distance estimate of 8.6 (+2.0,-1.6) kpc and a revised estimate for the mass of the black hole of 12.4 (+2.0,-1.8) Msun. GRS 1915+105 is at about the same distance as some HII regions and water masers associated with high-mass star formation in the Sagittarius spiral arm of the Galaxy. The absolute proper motion of GRS 1915+105 is -3.19 +/- 0.03 mas/y and -6.24 +/- 0.05 mas/y toward the east and north, respectively, which corresponds to a modest peculiar speed of 22 +/-24 km/s at the parallax distance, suggesting that the binary did not receive a large velocity kick when the black hole formed. On one observational epoch, GRS 1915+105 displayed superluminal motion along the direction of its approaching jet. Considering previous observations of jet motions, the jet in GRS 1915+105 can be modeled with a jet inclination to the line of sight of 60 +/- 5 deg and a variable flow speed between 0.65c and 0.81c, which possibly indicates deceleration of the jet at distances from the black hole >2000 AU. Finally, using our measurements of distance and estimates of black hole mass and inclination, we provisionally confirm our earlier result that the black hole is spinning very rapidly.Comment: 20 pages; 2 tables; 6 figure