  The effect of the up-conversion of the electronic energy level occupation was
earlier interpreted as an implication of the multiple scattering of the charge
carriers on the longitudinal optical phonons of the lattice vibrations in a
small system like a quantum dot. In this work we study the influence of this
effect on the electronic motion in a nanotransistor represented by a quantum
dot connected to two electric wires and a gate electrode. We show that in an
asymmetric nanotransistor the up-conversion effect gives rise to a spontaneous
current between the source and the drain, or to an appearance of a spontaneous
voltage between these electrodes. The effect will be studied basing on the well
known Datta's Toy Model of the theoretical description of the nanotransistor
and on additional kinetic equations giving the multiple scattering of electrons
in the quantum dot, in the self-consistent Born approximation to the electronic
self-energy. We shall also briefly discuss the relation of this theoretical
result to existing experiments on current-voltage characteristics in gated
nanostructures.
