The original motivation of great interest to topological insulators was the hope to observe the quantum spin Hall
effect. Therefore if a material is in the topological insulator state they frequently call it the quantum spin Hall
state. However, despite impressive experimental results confirming the existence of the quantum spin Hall state,
the quantum spin Hall effect has not yet been detected. After a short overview of what was originally suggested
as the quantum spin Hall effect (quantum spin conductance determined by the topological Chern number) the
paper analyzes the crucial role of the boundary condition on the observation of the effect and finally discusses
whether and how the quantum spin Hall effect could be observed.
Small Josephson junctions are known to be very susceptible to noise. We have utilized this property in developing methods to measure noise as well as environmental resonance modes in mesoscopic systems. We review recent results on tunnel junction systems and show also that higher order moments of shot noise can be addressed with the present method based on the noise-induced modification of incoherent tunneling of Cooper pairs.