  We compare two approaches to open quantum systems, namely, the non-Hermitian
dynamics and the Lindblad master equation. In order to deal with more general
dissipative phenomena, we propose the unified master equation that combines the
characteristics of both of these approaches. This allows us to assess the
differences between them as well as to clarify which observed features come
from the Lindblad or the non-Hermitian part, when it comes to experiment. Using
a generic two-mode single-atom laser system as a practical example, we
analytically solve the dynamics of the normalized density matrix operator. We
study the two-level model in a number of cases (depending on parameters and
types of dynamics), compute different observables and study their physical
properties. It turns out that one is able not only to describe the different
types of damping in dissipative quantum optical systems but also to mimic the
undamped anharmonic oscillatory phenomena which happen in quantum systems with
more than two levels (while staying within the framework of the analytically
simple two-mode approximation).
