Simple finite-dimensional model of the metastable state

TL;DR

This paper presents a simple finite-dimensional matrix model that effectively captures key properties of metastable states, including line shape, decay dynamics, and density of states, verified through numerical calculations.

Contribution

It introduces an approximate analytical solution for a special finite-dimensional matrix, serving as a simple, effective model of metastable states, analogous to the Fano formalism.

Findings

Reproduces key properties of metastable states

Validated by numerical calculations

Provides a simple analytical framework

Abstract

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.