582 research outputs found
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
Colorings of Hamming-Distance Graphs
Hamming-distance graphs arise naturally in the study of error-correcting codes and have been utilized by several authors to provide new proofs for (and in some cases improve) known bounds on the size of block codes. We study various standard graph properties of the Hamming-distance graphs with special emphasis placed on the chromatic number. A notion of robustness is defined for colorings of these graphs based on the tolerance of swapping colors along an edge without destroying the properness of the coloring, and a complete characterization of the maximally robust colorings is given for certain parameters. Additionally, explorations are made into subgraph structures whose identification may be useful in determining the chromatic number
Cross-Section Fluctuations in Chaotic Scattering
For the theoretical prediction of cross-section fluctuations in chaotic
scattering, the cross-section autocorrelation function is needed. That function
is not known analytically. Using experimental data and numerical simulations,
we show that an analytical approximation to the cross-section autocorrelation
function can be obtained with the help of expressions first derived by Davis
and Boose. Given the values of the average S-matrix elements and the mean level
density of the scattering system, one can then reliably predict cross-section
fluctuations
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
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