ИСТИНА

We deal with the Schr¨odinger operator H = −h ^2∆/2 +V (x) in the semi-classical limit describing the interacting pair of particles moving in the two-dimensional periodic trigonally symmetric potential field. Namely, we assume that V (x) = U0(x1, x2) + U0(x3, x4) + U1(x), where U0 is periodic on a 2D lattice and has a trigonal symmetry, and U1(x) describes the interaction between two particles. We discuss the asymptotics as h → 0 for the ground state spectral band widths as well as the dispersion relations between energy and quasi-momentum and the form of Bloch functions. Studying this sort of quantum systems called the ‘rotating dimers’ was proposed by M. I. Katsnelson and motivated by the physics of graphene. The work was supported by the Russian Foundation for Basic Research (grant № 18-31-00273).