Tunnelling and switching phenomena in superconducting quantum dots and Josephson junctions

This work is devoted to investigation of tunnelling and switching phenomena arising in Condensed Matter Physics. In the first part I investigate quantum tunnelling of a single Abrikosov vortex in a superconducting quantum dot. The escape of a vortex carrying magnetic flux leads to a switching of a quantum dot to non-magnetic state. Tunnelling of a vortex manifests itself as a spontaneous relaxation of magnetization. I showed that it is possible to use an instanton technique based on path integral formalism even in presence of forces breaking time-reversal symmetry. [Continues.]