Chaos simplifies quantum friction. (arXiv:1812.02649v1 [quant-ph])
By means of studying the evolution equation for the Wigner distributions of
quantum dissipative systems we derive the quantum corrections to the classical
Liouville dynamics, taking into account the standard quantum friction model.
The resulting evolution turns out to be the classical one plus fluctuations
that depend not only on the $\hbar$ size but also on the momentum and the
dissipation parameter (i.e. the coupling with the environment). On the other
hand, we extend our studies of a paradigmatic system based on the kicked
rotator, and we confirm that by adding fluctuations only depending on the size
of the Planck constant we essentially recover the quantum behaviour. This is
systematically measured in the parameter space with the overlaps and
differences in the dispersion of the marginal distributions corresponding to
the Wigner functions. Taking into account these results and analyzing the
Wigner evolution equation we propose that the chaotic nature of our system is
responsible for the independence on the momentum, while the dependence on the
dissipation is provided implicitly by the dynamics.