46 Nauky Ave.,

03028 Kyiv,

UKRAINE

and

Universita di Palermo,

Via Archirafi 36,

I-90123 Palermo,

ITALY

E-mail: lukyanets_s@ukr.net, messina@fisica.unipa.it

**Solving the master equation of a couple of interacting
complex subsystems coupled to a bosonic bath**

**Abstract:**

The dynamics of two two-level interacting atoms coupled to common electro-magnetic
bath closely located inside a lossy cavity is reportedfor different form
of the interaction symmetry. Initially injecting only one excitation in
the two dipole-dipole interacting atoms and cavity system, loss mechanisms
asymptotically drive the mater system toward a stationary maximally entangled
state. The role played by the closeness of the two atoms, with respect
to such a cooperative behavior, is carefully discussed. Stationary radiation
trapping effects are found and transparently interpreted. Ising-type interaction
between atoms causes another form of cooperative dynamics which is similar
to the superradiance effect. In the case of strong interaction, the coupling
between the mater sample and cavity mode has multi-photon character which
is to be displayed in the two-photon two-atom Rabi oscillation. From
a mathematical point of view we presentour successful approach relying
on the choice of a unitary transformation which accomplishes the passage
to a simple exactly solvable master equation.