  We make an adaptation of laser modelling equations to describe the behavior
of a phonon laser (saser). Our saser consists of an AlGaAs/GaAs double barrier
heterostructure designed to generate an intense beam of transversal acoustic
(TA) phonons. To study our system, we begin with a Hamiltonian that describes
the decay of primary longitudinal optical phonons (LO_1) into secondary (LO_2)
and TA (LO_1 -> LO_2 + TA) and its inverse process (recombination). Using this
Hamiltonian, a set of coupled equations of motion for the phonons is obtained.
We also consider the interaction between the phonons and its reservoirs. These
interactions are introduced in the equations of motion leading to a set of
coupled Langevin equations. In order to obtain an expression to describe our
saser we apply, in the Langevin equations, an adiabatic elimination of some
variables of the subsystem. Following the method above we obtain the value of
the injection threshold for the operation of our phonon laser. At this
threshold occurs a phase transition from a disordered to a coherent state. It
is shown that it is not necessary a big "optical" pumping to get a sasing
region.

Mesoscale and Nanoscale Physics