  Longitudinal optical phonons have been used to interpret the electronic
energy relaxation in quantum dots and at the same time they served as a
reservoir, with which the electronic subsystem is in contact. Such a phonon
subsystem is expected to be passive, namely, in a long-time limit the whole
system should be able to achieve such a stationary state, in which statistical
distributions of both subsystems do not change in time. We pay attention to
this property of the LO phonon bath. We show the passivity property of the so
far used approximations to electronic transport in quantum dots. Also we show a
way how to improve the passivity of LO phonon bath using canonical Lang-Firsov
transformation.
