Quantum effects induced by external fields and topology in field theory and in physics of condensed media

The influence of spatial curvature, topology and boundaries on physical characteristics of quantum fields will be investigated. As such characteristics, the expectation values of the field squared and energy-momentum tensor will be considered. For charged fields, the charge and current densities will be discussed as well. In a part of the problems the presence of a topological defect of the cosmic string type will be assumed. As background geometries we will consider the Minkowski, de Sitter and anti-de Sitter spacetimes with compact spatial dimensions in the presence of boundaries with different geometries. The applications of the obtained results in graphene made structures and in braneworld models will be discussed. Another part of the project is devoted to the construction and solutions of the low-dimensional quantum spin models. We are going to use these models for investigation of a number of phenomena in strongly correlated systems, magnetocaloric effect, magnetoelectric effect, localized state and others. The ground-state degeneracy, quantum numbers, topological phases of spin and fermionic systems with high-rank symmetries will be studied. Finally, the dynamical symmetries of superintegrable systems of interacting quantum particles will be investigated.