A Simple Finite-Dimensional Model of the Metastable State

We have constructed an approximate analytical solution to the spectral problem for a finite-dimensional matrix of a special form, which proves to be a very simple and sufficiently satisfactory model of the metastable state. This model reproduces most of the characteristic properties of the metastable state, including the line shape, decay dynamics, and density of states. The accuracy of the approximate analytical solution was verified through direct numerical calculations. The proposed model represents a finite-dimensional analog of the Fano formalism.