Spectroscopic studies in open quantum systems

The Hamiltonian H of an open quantum system is non-Hermitian. Its complex e igenvalues ER are the pales of the S matrix and provide bath the energies a nd widths of the states. We illustrate the interplay between Re(H) and Im(H ) by means of the different interference phenomena between two neighboring resonance states. Level repulsion may occur along the real or imaginary axi s (the latter is called resonance trapping). In any case, the eigenvalues o f the two states avoid crossing in the complex plane. We then calculate the poles of the S matrix and the corresponding wave functions for a rectangul ar microwave resonator with a scatter as a function of the area of the reso nator as well as of the degree of opening, to a waveguide. The calculations are performed by using the method of exterior complex scaling. Re(H) and I m(H) cause changes in the structure of the wave functions which are permane nt, as a rule. The resonance picture obtained from the microwave resonator shows all the characteristic features known from the study of many-body sys tems in spite of the absence of two-body forces. The effects arising from t he interplay between resonance trapping and level repulsion along the real axis are not involved in the statistical theory (random matrix theory).