Simple finite-dimensional model of the metastable state

We have constructed an approximate analytical solution of the spectral problem for a finite-dimensional matrix of a special kind, which turns out to be a very simple and quite satisfactory model of the metastable state. Most of the characteristic properties of the metastable state are reproduced: line shape, decay dynamics, and density of states. The correctness of the approximate analytical solution was verified by direct numerical calculations. The proposed model is a finite-dimensional analog of the Fano formalism.