This thesis considers dynamic phenomena in transport through electronic devices on sub-micron scale. It consists of two closely related parts, the first considering DC current through a quantum dot as a response to a periodic perturbation of its shape and the second, conversely, explores a finite-frequency spin wave in a ferromagnet due to a constant electric current. Both systems are very similar in their theoretical treatment by scattering matrix formalism.

The Chapters \ref{chap:2}--\ref{chap:4} consider a charge current induced by a periodic perturbation of an open quantum dot's shape. A dot being mesoscopic, its transport properties strongly fluctuate from sample to sample and therefore knowledge of full sample-to-sample distributions is essential. We consider a ``quantum pumping" regime of reservoirs in equilibrium and periodic variation of the dot's shape by AC voltages applied at the gates. Experimentally measurable first several moments of mesoscopic distribution of charge pumped in one cycle are explored.

Chapter \ref{chap:2} considers distributions of adiabatically pumped current $I¯$ and voltage $V¯$ and finds that even in a slow weak pumping regime they are not simply related via time-averaged conductance $G¯$. Moreover, values of $I¯-V¯G¯$ for few-channel dots exhibit strong mesoscopic fluctuations, comparable with those of $I¯$.% and $V¯$.

Chapter \ref{chap:3} explores mesoscopic distributions of noise and current-to-noise ratio in a weak pumping regime in a wide region of temperatures and pumping frequencies. Fluctuations of noise in the multi-channel limit $N\to \infty$ are found to be small as $1/N$. For a multi-channel system the ensemble-averaged noise is analytically found and calculated for experimentally relevant temperatures, frequencies and pumping strengths.

The Chapter \ref{chap:4} concerns the formalism of time-dependent scattering matrix theory and finds correlators of matrix elements up to the fourth order. Our findings allow a systematic treatment of various transport properties, as well as their ensemble-averaged correlations. We also compare our results with results obtained in Hamiltonian approach of Random Matrix theory.

The second part, Chapter \ref{chap:5}, considers magneto-transport through a single ferromagnetic layer. Electric current flowing perpendicular to the plane of a thin layer is shown to excite a finite frequency response in form of a spin wave. Unlike the previously known spin-torque due to a polarized current, another mechanism able to induce a destabilizing torque on a local magnetization is found. Spin-diffusion of reflected spins from one point on the normal-ferromagnet boundary to another might excite a spin wave at sufficiently strong currents. We analytically find the critical current value and discuss our results for experimentally relevant parameters.