Thouless energy of a superconductor from non local conductance fluctuations

We show that a spin-up electron from a normal metal entering a superconductor propagates as a composite object consisting of a spin-down hole and a pair in the condensate. This leads to a factorization of the non local conductance as two local Andreev reflections at both interfaces and one propagation in the superconductor, which is tested numerically within a one dimensional toy model of reflectionless tunneling. Small area junctions are characterized by non local conductance fluctuations. A treatment ignoring weak localization leads to a Thouless energy inverse proportional to the sample size, as observed in the numerical simulations. We show that weak localization can have a strong effect, and leads to a coupling between evanescent quasiparticles and the condensate by Andreev reflections internal to the superconductor.