Continuum shell model and nuclear physics at the edge of stability

Studies of nuclei far from the valley of stability are currently in the center of modern nuclear physics. For such loosely bound systems, the continuum effects are vitally important. We develop the continuum shell model based on an effective non-Hermitian Hamiltonian. This rigorous quantum-mechanical method is powerful for description of open quantum systems unifying their structure and reactions. The formalism is explained and examples of its application are given; the results are in a very good agreement with recent experiments on exotic nuclei. We show also how this approach can be successfully applied to a general problem of a signal transmission through an open quantum system.