Stellar migration in galaxy discs using the Chirikov diffusion rate

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.