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The impact of quantum effects on relativistic electron motion in a chaotic regime

We consider the impact of quantum effects on electron dynamics in a plane linearly polarized standing wave with relativistic amplitudes. For this purpose analysis the Lyapunov characteristic exponent spectrum with and without allowance for the classic radiation reaction force has been analyzed. Based on this analysis it is concluded that the contraction effect of phase space in the stochastic regime due to the radiation reaction force in the classical form doesn't occur when the quantum nature of hard photon emission is taken into account. It is shown that electron bunch kinetics has a diffusion solution rather than the d'Alambert type solution as in the classic description.It is also revealed that the electron motion can be described using the Markov chain formalism. This method gives exact characteristics of electron bunch evolution, such as motion of the center of mass and electron bunch dimensions.