After a short abstract introduction on the time evolution driven by non-self-adjoint Hamiltonians, we show how the recently introduced concept of pseudo-fermion can be used in the description of damping in finite dimensional quantum systems, and we compare the results deduced adopting the Schrodinger and the Heisenberg representations. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790514]