Results of 2DMonte-Carlo simulations of development of QED cascades in intense uniformly rotating electric field
are presented. We consider cascades produced by initially slow electrons. It is shown that under such conditions
stable cascade development starts at field strength of the order of 1% of the QED critical field 5 × 10<sup>29</sup>W/cm<sup>2</sup>.
The cascade yield is growing exponentially in time. Several characteristics of cascade, including average energy of
particles and their mean free path times are computed. Our results are in good agreement with recent estimations
[A. M. Fedotov et al., PRL 105, 080402 (2010)].
We present a new class of exact nonsingular solutions for the Maxwell equations in vacuum, which describe the
electromagnetic field of the counterpropagating focused laser beams and the subperiod focused laser pulse. These
solutions are derived by the use of a modification of the "complex source method", investigated and visualized.
It is argued that, unlike the case of the mutual trapping of several light beams, the selftrapping of a single light
beam in the vacuum due to vacuum polarization would require the field strengths much greater than 10<sup>16</sup>V/cm
and hence can not be observed in the foreseeable future.
An atom interacting with a quantized electromagnetic field in a cavity with time-dependent parameters is considered. Variation of the cavity parameters results in excitation of the atom, even if photons were initially absent in the cavity. We study a new mechanism of atom excitation and photon creation inside the cavity which we call the dynamical Lamb effect, and which has no relation to the dynamical Casimier effect. Several aspects of this mechanism are studied, including physical interpretation, amplification of the amplitude in the case of long-time periodic variation of the cavity parameters, and possible physical realization. Although the consideration is based mainly on a simple model of an atom interacting with a single mode of quantized electromagnetic field, and the results are qualitatively valid for more realistic models.