The states of an open quantum system are coupled via the environment of scattering wave functions. The complex coupling coefficients $\omega$ between system and environment arise from the principal value integral and the residuum. At high-level density where the resonance states overlap, the dynamics of the system is determined by exceptional points. At these points, the eigenvalues of two states are equal and the corresponding eigenfunctions are linearly dependent. It is shown in the present paper that Im$\left(\omega \right)$ and Re$\left(\omega \right)$ influence the system properties differently in the surrounding of exceptional points. Controlling the system by a parameter, the eigenvalues avoid crossing in energy near an exceptional point under the influence of Re$\left(\omega \right)$ in a similar manner as it is well known from discrete states. Im$\left(\omega \right),$ however, leads to width bifurcation and finally (when the system is coupled to one channel, i.e., to one common continuum of scattering wave functions), to a splitting of the system into two parts with different characteristic time scales. The role of observer states is discussed. Physically, the system is stabilized by this splitting since the lifetimes of some states are longer than before, while that of one state is shorter. In the cross section the short-lived state appears as a background term in high-resolution experiments. The wave functions of the long-lived states are mixed in those of the original ones in a comparably large parameter range. Numerical results for the eigenvalues and eigenfunctions are shown for $N=2,4,$ and 10 states coupled mostly to one channel.

• Received 11 March 2013

DOI:https://doi.org/10.1103/PhysRevE.87.052136