Exactly soluble model of the time-resolved fluorescence return to thermal equilibrium in many-particle systems after excitation

In this paper we consider the assembly of weakly interacting identical particles, where the occupation of single-particle energy-levels at thermal equilibrium is governed by statistics. The analytic form of the inter-energy-level jump matrix is derived and analytic solution of the related eigen-problem is given. It allows one to demonstrate the nature of decline in time of the energy emission (fluorescence, recombination) of such many-level system after excitation in a relatively simple and unifying way – as a multi-exponential de-excitation. For the system of L energy levels the number of the de-excitation lifetimes is L−1. The lifetimes depend on the energy level spectrum as a whole. Two- and three-level systems are considered in detail. The impact of the energy level degeneracy on the lifetimes is discussed.