  We are re-examining the problem of stellar migration in disc galaxies from a
diffusion perspective. We use for the first time the formulation of the
diffusion rates introduced by \citet{1979PhR....52..263C}, applied to both
energy $E$ and angular momentum $L_\mathrm{z}$ in self-consistent N$-$body
experiments. We limit our study to the evolution of stellar discs well after
the formation of the bar, in a regime of adiabatic evolution. We show that
distribution functions of Chirikov diffusion rates have similar shapes
regardless the simulations, but different slopes for energy and angular
momentum. Distribution functions of derived diffusion time scales $T_D$ have
also the same form for all simulations, but are different for $T_D(E)$ and
$T_D(L_\mathrm{z})$. Diffusion time scales are strongly dependent on
$L_\mathrm{z}$. $T_D(E) \lesssim 1$~Gyr in a $L_\mathrm{z}$ range roughly
delimited by the set of stellar bar resonances (between the Ultra Harmonic
Resonance and the Outer Lindblad Resonance). Only particles with low
$L_\mathrm{z}$ have $T_D(L_\mathrm{z}) \lesssim 10$ Gyr, i.e. the simulation
length. In terms of mass fraction, 35 to 42% turn out to diffuse energy in a
characteristic time scale shorter than 10 Gyr, i.e. simulations length, while
60 to 64% undergo the diffusion of the angular momentum on the same time scale.
Both the diffusion of $L_\mathrm{z}$ and $E$ are important in order to grasp
the full characterisation of the radial migration process, and we showed that
depending on the spatial region considered, one or the other of the two
diffusions dominates.
