International audienceWe investigate dynamics of charged particles in current sheets with the sheared magnetic field. In our previous paper (Artemyev et al., 2013) we studied the particle motion in such magnetic field configurations on the basis of the quasi-adiabatic theory and conservation of the quasi-adiabatic invariant. In this paper we concentrate on violation of the adiabaticity due to jumps of this invariant and the corresponding effects of stochastization of a particle motion. We compare effects of geometrical and dynamical jumps, which occur due to the presence of the separatrix in the phase plane of charged particle motion. We show that due to the presence of the magnetic field shear, the average value of dynamical jumps is not e...