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The states of an open quantum system are coupled via the environment ofscattering wavefunctions. The complex coupling coefficients $\omega$ betweensystem and environment arise from the principal value integral and theresiduum. At high level density where the resonance states overlap, thedynamics of the system is determined by exceptional points. At these points,the eigenvalues of two states are equal and the corresponding eigenfunctionsare linearly dependent. It is shown in the present paper that Im$(\omega)$ andRe$(\omega)$ influence the system properties differently in the surrounding ofexceptional points. Controlling the system by a parameter, the eigenvaluesavoid crossing in energy near an exceptional point under the influence ofRe$(\omega)$ in a similar manner as it is well known from discrete states.Im$(\omega)$ however leads to width bifurcation and finally (when the system iscoupled to one channel, i.e. to a common continuum of scatteringwavefunctions), to a splitting of the system into two parts with differentcharacteristic time scales. Physically, the system is stabilized by thissplitting since the lifetimes of most ($N-1$) states are longer than beforewhile that of only one state is shorter. In the cross section the short-livedstate appears as a background term in high-resolution experiments. Thewavefunctions of the long-lived states are mixed in those of the original onesin a comparably large parameter range. Numerical results for the eigenvaluesand eigenfunctions are shown for $N=2, ~4$ and 10 states coupled mostly to 1channel.

Width bifurcation and dynamical phase transitions in open quantum systems