Incompatibility of different customary kaon phase convention

The conventions that Wu and Yang assumed for the kaon phases in the context of $CP$ symmetrical two-pion decay channels fix the relative kaon phase. This fact, apparently not emphasized sufficiently in the past, has recently been overlooked by Hayakawa and Sanda. In particular, Wu and Yang fix the relative phase to a different value than the one resulting from the convention $CP|K^{0}\rangle = |\overline{K^{0}}\rangle$. The difference between the two values is made up of possible contributions from $CPT$- and direct $CP$-violations during the decay of a kaon into a two-pion state of isospin zero.Comment: 5 pages, LaTe

Raman spectroscopy with ultrashort coherent excitation. Narrowing of spectral lines beyond the dephasing linewidth

Spectroscopists are constantly faced with the task of improved spectral resolution. Two points are of major interest: (i) The precise frequency of the quantized transition and (ii) the detection of new neighboring transitions. Besides experimental factors the ultimate spectral resolution is determined by the inherent linewidth of the transition. Optical spectroscopists have to deal with different line-broadening processes; for instance with the Doppler effect or with collision broadening in gases, with dephasing processes in condensed systems and with the population relaxation which results in the natural linewidth. In recent years, different novel techniques have been devised which provide spectral resolution beyond the transition linewidth. For instance, Doppler broadening can be eliminated by saturation spectroscopy or by two counter-propagating beams for two-photon transitions/I/. Even measurements beyond the natural linewidth have been performed taking biased signals from the fluorescent decay /2-5/. Techniques have been proposed where the difference between the decay rates of the two states rather than their sum determines the linewidth /6,7/, and narrowing of the natural linewidth by decaying-pulse excitation has been discussed /8/. Very recently, we have demonstrated substantial line narrowing of Raman type transitions in condensed phases /9-11/. The lines were broadened by vibrational dephasing. New information was obtained in congestedspectral regions

The Minispiral in the Galactic Center revisited

We present the results of a re-examination of a [Ne II] line emission data cube (\lambda 12.8 \mu m) and discuss the kinematic structure of the inner \sim 3 \times 4 pc of the Galaxy. The quality of [Ne II] as a tracer of ionized gas is examined by comparing it to radio data. A three dimensional representation of the data cube allows us to disentangle features which are projected onto the same location on the sky. A model of gas streams in different planes is fitted to the data. We find that most of the material is located in a main plane which itself is defined by the inner edge of the Circum-Nuclear Disk in the Galactic Center. Finally, we present a possible three dimensional model of the gas streams.Comment: 12 pages, 18 figures; submitted to New Astronomy; higher resolution version and two animations available via anonymous ftp ftp://ftp.ita.uni-heidelberg.de/pub/ITA/wjd/Minispira

Redundancy of minimal weight expansions in Pisot bases

Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer $n$ as a sum $n=\sum_k \epsilon_k U_k$, where the digits $\epsilon_k$ are taken from a finite alphabet $\Sigma$ and $(U_k)_k$ is a linear recurrent sequence of Pisot type with $U_0=1$. The most prominent example of a base sequence $(U_k)_k$ is the sequence of Fibonacci numbers. We prove that the representations of minimal weight $\sum_k|\epsilon_k|$ are recognised by a finite automaton and obtain an asymptotic formula for the average number of representations of minimal weight. Furthermore, we relate the maximal order of magnitude of the number of representations of a given integer to the joint spectral radius of a certain set of matrices