We present a simple exactly solvable extension of of the Jaynes-Cummings model by adding dissipation. This is done such that the total number of excitations is conserved. The Liouville operator in the resulting master equation can be reduced to blocks of 4×4 matrices.
Cite
@article{arxiv.1110.2139,
title = {Decoherence at constant excitation},
author = {Juan Mauricio Torres and Emerson Sadurni and Thomas H. Seligman},
journal= {arXiv preprint arXiv:1110.2139},
year = {2012}
}