Parametric resonance and particle stochastic interactions with a periodic medium

A non-markovian stochastic model shows the emergence of structures in the medium, a self-organization characterized by a relationship between particle's energy, driven frequency $\omega$ and a frequency of interaction with the medium $\nu$. The interaction determines its mass and this fine tuning results in an effective force given by $F_L=\hbar \omega^2 n(\lambda)/ c$, similar to the interaction force between photons and atoms. Condition for the particle-medium resonance is determined, with relevance to detect dark matter axion-like particles and the parametric resonance as a pop-up mechanism to turn fields into particles.