Vlasii N. Application of the field-theoretical methods to low-dimensional quantum systems at finite temperature.

This thesis concerns This thesis concerns to theoretical investigation of physical properties low-dimensional systems of quasirelativistic fermions, which are quantiezed in the external field of topological defect. We compute the thermal quadratic fluctuation of total angular momentum and thermal correlations of total angular momentum with spin and orbital angular momentum in planar relativistic Fermi gas with a pointlike magnetic vortex. It is established that depending on the choice of a boundary condition at the location of a magnetic vortex the vacuum value of the total angular momentum can be either sharp quantum observable in each individual quantum measurement or average by a lot of quantum measurements. It is shown that a topological defect in graphene that rolls up a graphitic sheet into a nanocone is described by a pseudomagnetic vortex at the apex of the cone. We derive the analytical expressions for the density of states in cases of all possible disclination. It is shown that in the presence of defects in graphene such as one-pentagon, one-heptagon, and three-heptagona unit of charge can be induced in the ground state.