Rotter I
Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036213. doi: 10.1103/PhysRevE.64.036213. Epub 2001 Aug 27.
A relation between the eigenvalues of an effective Hamilton operator and the poles of the S matrix is derived that holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with two-body forces between the constituents or it may be a quantum billiard without any two-body forces. Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points in the complex plane. Under certain conditions, these branch points appear as double poles of the S matrix. They influence the dynamics of open as well as of closed quantum systems. The dynamics of the two-level system is studied in detail analytically as well as numerically.
