We introduce a variant of the replica trick within the nonlinear sigma model that allows calculating the distribution function of the persistent current. In the diffusive regime, a Gaussian distribution is derived. This result holds in the presence o
f local interactions as well. Breakdown of the Gaussian statistics is predicted for the tails of the distribution function at large deviations.
We investigate theoretically charge transport in hybrid multiterminal junctions with superconducting leads kept at different voltages. It is found that multiple Andreev reflections involving several superconducting leads give rise to rich subharmonic
gap structures in the current-voltage characteristics. The structures are evidenced numerically in junctions in the incoherent regime.
The Josephson current in a diffusive superconductor/ferromagnet/superconductor junction with precessing magnetization is calculated within the quasiclassical theory of superconductivity. When the junction is phase-biased, a stationary current (withou
t a.c. component) can flow through it despite the non-equilibrium condition. A large critical current is predicted due to a dynamically induced long range triplet proximity effect. Such effect could be observed in a conventional hybrid device close to the ferromagnetic resonance.
We study the Josephson current through a ferromagnetic trilayer, both in the diffusive and clean limits. For colinear (parallel or antiparallel) magnetizations in the layers, the Josephson current is small due to short range proximity effect in super
conductor/ferromagnet structures. For non colinear magnetizations, we determine the conditions for the Josephson current to be dominated by another contribution originating from long range triplet proximity effect.
