1.Laser radiation is a unique tool that makes it pos sible to efficiently control both the internal quantum state of atoms and their external degrees of freedom. The latter underlies laser cooling of atoms and ions, which is a modern field of quantum physics that is at the boundary between atomic optics and laser physics (see, e.g., [1][2][3][4][5]). Gradually increasing interest in this field is primarily due to numerous implemented diverse exciting applications of laser cooling and trap ping of atoms. Of particular interest are wide prospects of its application in fundamental quantum metrology, where laser cooled atoms are the main candidates for creating a new generation of optical frequency and time standards [6] with a very high accuracy (relative error as small as 10 -18 -10 -17 ) [7][8][9]. Laser cooling has important applications in atomic interferometry, implementation of Bose-Einstein condensation, quantum informatics, and atomic nanolithography.Various methods of laser cooling and localization of atoms (magneto optical trap, optical grating, dipole traps of various configurations, etc.) have already been developed, which make it possible to cool atoms to ultralow temperatures (to hundreds of nanokelvin). It is quite difficult to theoretically describe the kinetics of cold atoms in laser fields. For this reason, various approximations are often used. In particular, the main mechanisms of laser cooling and trapping were under stood using a two level model of atom with nondegen erate energy levels [1,2]. This model under certain conditions corresponds to real atoms with a F g = 0 F e = 1 transition. Although the two level model is con sidered to be well studied, some aspects remain unan alyzed. Indeed, even in this simplest system, addi tional simplifications are used, assuming that the stan dard deviation of atomic momenta is much higher than the momentum of a photon, i.e., បk/Δp a Ӷ 1 (the so called semiclassical approximation [2, 10]). Then, neglecting the spatial localization of atoms in the opti cal potential (at a scale of the light wavelength), an approximate Fokker-Planck equation for the momentum distribution function of atoms is consid ered rather than the exact equation for the density matrix.Concerning the spatial location of atoms in the field of a standing light wave, it is well known that atoms in weak fields are concentrated near minima of the optical potential [1,2]. In the case of red frequency detuning (when the laser frequency is lower than the frequency of an atomic transition) and blue frequency detuning, the minima of the optical potential coincide with the antinodes and nodes of the field, respectively. However, the regime of a moderate light field and red frequency detuning has not yet been analyzed from this point of view. In particular, a new effect-the anomalous concentration of atoms outside of the min ima of the optical potential and, the more so, at the maxima of the potential-is revealed in this work. This counterintuitive behavior of atoms appears to be The stationary mome...