We consider wide ballistic microcontacts with electron-electron scattering in the leads and calculate electric noise and nonlinear conductance in them. Due to a restricted geometry the collisions of electrons result in a shot noise even though they conserve the total momentum of electrons. We obtain the noise and the conductivity for arbitrary relations between voltage V and temperature T . The positive inelastic correction to the Sharvin conductance is proportional to T at low voltages eV ≪ T , and to |V | at high voltages. At low voltages the noise is defined by the Nyquist relation and at high voltages the noise is related with the inelastic correction to the current by the Shottky formula Sin = 2e Iin.

We investigate theoretically the non-local conductance through a superconducting wire in tunnel contact with normal and ferromagnetic leads. In the presence of an in-plane magnetic field, the superconducting density of states is spin-split, and the current injected from the normal lead is spin-polarized. A non-local conductance that is antisymmetric with the applied voltage can be measured with a ferromagnetic lead. It persists for a distance between the contacts that is larger than both the charge-imbalance relaxation length and the normal-state spin relaxation length. We determine its amplitude by considering two extreme models of weak and strong internal equilibration of the superconducting quasiparticles due to electron-electron interactions. We find that the nonlocal signal, which was measured in recent experiments and discussed as a spin-imbalance effect, can be interpreted alternatively as the signature of a thermoelectric effect.PACS numbers: 72.25. Ba, 74.25.fg, 74.40.Gh, Introduction.-Recent progress in the realization of complex ferromagnet/superconductor (F/S) heterostructures has lead to the emergence of "superconducting spintronics" as a promising field of research. A fundamental question concerns the ability of superconductors to sustain the flow of a spin-polarized current. A standard way to study spin injection and relaxation in a normal metal consists in contacting it with two ferromagnetic leads, an injector (I) and a detector (D), and measuring the dependence of the non-local conductance, g nl = ∂I D /∂V I , on their separation. Such a method was also used to measure the spin lifetime in superconductors [1][2][3]. Moderate variations of the spin lifetime in the superconducting state, with respect to its normal-state value, could be attributed to magnetic impurities [2] or weak spin-orbit coupling [3,4].