This review article describes theoretical and experimental advances in using quantum dots as a system for studying impurity quantum phase transitions and the non-Fermi liquid behavior at the quantum critical point.
We propose ways to create and detect fractionally charged excitations in emph{integer} quantum Hall edge states. The charge fractionalization occurs due to the Coulomb interaction between electrons propagating on different edge channels. The fraction
al charge of the soliton-like collective excitations can be observed in time resolved or frequency dependent shot noise measurements.
We study theoretically the contribution of fluctuating Cooper pairs to the persistent current in superconducting rings threaded by a magnetic flux. For sufficiently small rings, in which the coherence length $xi$ exceeds the radius $R$, mean field th
eory predicts a full reduction of the transition temperature to zero near half-integer flux. We find that nevertheless a very large current is expected to persist in the ring as a consequence of Cooper pair fluctuations that do not condense. For larger rings with $Rgg xi$ we calculate analytically the susceptibility in the critical region of strong fluctuations and show that it reflects competition of two interacting complex order parameters.
