Applicability of the approximate Langevin equation for describing the motion of nanospheres in the field of a standing light wave

Based on the Langevin equation, the motion of a transparent nanosphere in the field of a standing light wave of a continuous-wave laser radiation is investigated and the conditions for its localization (optical trap) at the maximum of the interference pattern of the field of two counterpropagating waves are determined. The scope of applicability of neglecting the second derivative in the Langevin equation, the so-called “reduced equation,” is found, the use of which gives the solution in an analytical form. The stability conditions for the localization of the nanosphere at the maximum of the interference pattern of the field are determined depending on the kinetic energy of its thermal (Brownian) motion.