Time Reversal and Exceptional Points

Eigenvectors of decaying quantum systems are studied at exceptional points of the Hamiltonian. Special attention is paid to the properties of the system under time reversal symmetry breaking. At the exceptional point the chiral character of the system -- found for time reversal symmetry -- generically persists. It is, however, no longer circular but rather elliptic.Comment: submitted for publicatio

The Chirality of Exceptional Points

Exceptional points are singularities of the spectrum and wave functions which occur in connection with level repulsion. They are accessible in experiments using dissipative systems. It is shown that the wave function at an exceptional point is one specific superposition of two wave functions which are themselves specified by the exceptional point. The phase relation of this superposition brings about a chirality which should be detectable in an experiment.Comment: four pages, one postscript figure, to be submitted to PR

Development of an integrated set of research facilities for the support of research flight test

The Ames-Dryden Flight Research Facility (DFRF) serves as the site for high-risk flight research on many one-of-a-kind test vehicles like the X-29A advanced technology demonstrator, F-16 advanced fighter technology integration (AFTI), AFTI F-111 mission adaptive wing, and F-18 high-alpha research vehicle (HARV). Ames-Dryden is on a section of the historic Muroc Range. The facility is oriented toward the testing of high-performance aircraft, as shown by its part in the development of the X-series aircraft. Given the cost of research flight tests and the complexity of today's systems-driven aircraft, an integrated set of ground support experimental facilities is a necessity. In support of the research flight test of highly advanced test beds, the DFRF is developing a network of facilities to expedite the acquisition and distribution of flight research data to the researcher. The network consists of an array of experimental ground-based facilities and systems as nodes and the necessary telecommunications paths to pass research data and information between these facilities. This paper presents the status of the current network, an overview of current developments, and a prospectus on future major enhancements

Chaotic Scattering in the Regime of Weakly Overlapping Resonances

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function if S to a theoretical expression based on random--matrix theory. We find very good agreement below but not above 10.1 GHz

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

Quantum Chaotic Scattering in Microwave Resonators

In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for resonators with and without time-reversal invariance. Statistical measures for S-matrix fluctuations were determined from the data and compared with extant and/or newly derived theoretical results obtained from the random-matrix approach to quantum chaotic scattering. The latter contained a small number of fit parameters. The large data sets taken made it possible to test the theoretical expressions with unprecedented accuracy. The theory is confirmed by both, a goodness-of-fit-test and the agreement of predicted values for those statistical measures that were not used for the fits, with the data

A Robust Path Tracking Algorithm for Homotopy Continuation

Conventional path tracking algorithms used in homotopy continuation systems sometimes miss roots owing to jumping from one segment of the homotopy path to another even if there exists homotopy paths to the roots. A robust path tracking algorithm is proposed which loses significant efficiency only on those portions of the path where segment jumping is likely to occur. The method presented here basically performs the predictor-corrector procedure using the Euler predictor and the Newton corrector. Any available algorithm can be used to control the step size. Robustness is achieved by adding the following rule: control the step size so that each continuation step causes a reasonably small change in the determinant of the augmented Jacobian. Case studies have shown that allowing -50 to +100% change virtually eliminates segment jumping in all the path-tracking algorithms tested. The determinant monitoring step size control algorithm can be applied to most of the currently available path tracking algorithms so that extremely tangled homotopy paths can be traced, finding all roots on them. Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved

Evidence for Neutrinoless Double Beta Decay

The data of the Heidelberg-Moscow double beta decay experiment for the measuring period August 1990 - May 2000 (54.9813 kg y or 723.44 molyears), published recently, are analyzed using the potential of the Bayesian method for low counting rates. First evidence for neutrinoless double beta decay is observed giving first evidence for lepton number violation. The evidence for this decay mode is 97% (2.2\sigma) with the Bayesian method, and 99.8% c.l. (3.1\sigma) with the method recommended by the Particle Data Group. The half-life of the process is found with the Bayesian method to be T_{1/2}^{0\nu} = (0.8 - 18.3) x 10^{25} y (95% c.l.) with a best value of 1.5 x 10^{25} y. The deduced value of the effective neutrino mass is, with the nuclear matrix elements from [Sta90,Tom91] = (0.11 - 0.56) eV (95% c.l.), with a best value of 0.39 eV. Uncertainties in the nuclear matrix elements may widen the range given for the effective neutrino mass by at most a factor 2. Our observation which at the same time means evidence that the neutrino is a Majorana particle, will be of fundamental importance for neutrino physics. PACS. 14.69.Pq Neutrino mass and mixing; 23.40.Bw Weak-interaction and lepton (including neutrino) aspects 23.40.-s Beta decay; double beta decay; electron and muon capture.Comment: 14 pages, psfile, 7 figures, Published in Modern Physics Letters A, Vol. 16, No. 37 (2001) 2409-2420, World Scientific Publishing Company, Home Page: http://ejournals.wspc.com.sg/mpla/16/1637/S0217732301005825.html, Home Page of Heidelberg Non-Accelerator Particle Physics Group: http://www.mpi-hd.mpg.de/non_acc