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Approximation of the Second Order in Model of Charge Motion Under Magneto-Dimensional Resonance

Student: Aleksandr Lyubich

Supervisor: Mikhail Karasev

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2018

The main object of the study of the research is the Hamilton operator in the case of motion of a charged particle in a thin film under the influence of a magnetic field. The aim of the work is to find the effective Hamiltonian in the case when the magnetic field is inclined at a small angle to the perpendicular to the film. For this research was used the method of quantum averaging.As a result, the averaged Hamiltonian is explicitly written in the first two orders in angle of slope in the form of a quadratic function. Further, this operator is expressed in terms of generators of the symmetry algebra of the leading part of the Hamiltonian.

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