Inverse scattering problem for quantum graph vertices

We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or Fülöp-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities

Review of SIS Experimental Results on Strangeness

>A review of meson emission in heavy ion collisions at incident energies around 1 -- 2 $A\cdot$GeV is presented. It is shown how the shape of the spectra and the various particle yields vary with system size, with centrality and with incident energy. A statistical model assuming thermal and chemical equilibrium and exact strangeness conservation (i.e. strangeness conservation per collision) explains most of the observed features. Emphasis is put onto the study of $K^+$ and $K^-$ emission. In the framework of this statistical model it is shown that the experimentally observed equality of $K^+$ and $K^-$ rates at threshold corrected energies $\sqrt{s} - \sqrt{s_{th}}$ is due to a crossing of two excitation functions. Furthermore, the independence of the $K^+$ to $K^-$ ratio on the number of participating nucleons observed between 1 and 10 $A\cdot$GeV is consistent with this model. The observed flow effects are beyond the scope of this model.Comment: 10 pages, 9 figures, Strangeness 2000, V International Conference on Strangeness in Quark Matter, July, 2000, Berkeley, Californi

The strange-quark chemical potential as an experimentally accessible "order parameter" of the deconfinement phase transition for finite baryon-density

We consider the change of the strange-quark chemical potential in the phase diagram of nuclear matter, employing the Wilson loop and scalar quark condensate order parameters, mass-scaled partition functions and enforcing flavor conservation. Assuming the region beyond the hadronic phase to be described by massive, correlated and interacting quarks, in the spirit of lattice and effective QCD calculations, we find the strange-quark chemical potential to change sign: from positive in the hadronic phase - to zero upon deconfinement - to negative in the partonic domain. We propose this change in the sign of the strange-quark chemical potential to be an experimentally accessible order parameter and a unique, concise and well-defined indication of the quark-deconfinement phase transition in nuclear matter.Comment: 22 pages, 14 figures within text, 2 figures(6,B3) as separate files. To be published in J.Phys.G: Nucl.&Part.Phys. G28 (2002