Static and dynamic properties of small particles

The term "small particles" refers to the mesoscopic objects much larger than atomic scale (usually about 1A) but smaller than 1{dollar}mu{dollar}. The research in this size range is inspired both by technical necessity to create miniature devices and by new interesting phenomena revealed when the quantization of the internal degrees of freedom is emphasized by the extremely small size. In this thesis mostly the two-dimensional case is studied, which has relevance to modern artificial objects.; The first part of this thesis covers the topics related to fluctuations of the charging energy of semiconductor quantum dots. Special emphasis is made on the case of crystalline quantum dots (islands) in both disordered (Coulomb glass) and clean case, when electrons form Wigner crystal. The latter case can occur e.g. when extremely strong magnetic field is applied perpendicular to the plane of the island. The second part treats superconductor vortex cores as small particles. The structure and dynamics of vortices is an important issue of superconductivity because motion of vortices determines losses and limits high-current applications of superconducting wires and cavities. The dissipation in the process of vortex motion occurs inside vortex cores where normal electrons remain even at low temperatures. Therefore we present the study of dissipation in the mixed state of the superclean layered type II superconductors mediated by the excitations within vortex cores.