  Stochasticity effects in the spin (de)polarization of an ultrarelativistic
electron beam during photon emissions in a counterpropoagating ultrastrong
focused laser pulse in the quantum radiation reaction regime are investigated.
We employ a Monte Carlo method to describe the electron dynamics
semiclassically, and photon emissions as well as the electron radiative
polarization quantum mechanically. While in the latter the photon emission is
inherently stochastic, we were able to identify its imprints in comparison with
the new developed semiclassical stochasticity-free method of radiative
polarization applicable in the quantum regime. With an initially spin-polarized
electron beam, the stochastic spin effects are seen in the dependence of the
depolarization degree on the electron scattering angle and the electron final
energy (spin stochastic diffusion). With an initially unpolarized electron
beam, the spin stochasticity is exhibited in enhancing the known effect of
splitting of the electron beam along the propagation direction into two
oppositely polarized parts by an elliptically polarized laser pulse. The
considered stochasticity effects for the spin are observable with currently
achievable laser and electron beam parameters.
