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Recent experiments on mesoscopic normal-metal-superconductor heterostructures resolve properties on length scales and at low temperatures such that the temperature is below the Thouless energy k B T ≤ E Th . We describe the properties of these systems within the framework of quasiclassical many-body techniques. Diffusive and ballistic systems are covered, both in equilibrium and nonequilibrium situations. Thereby we demonstrate the common physical basis of various subtopics.

Golubev and Zaikin Reply: In their Comment [1], Aleiner, Altshuler, and Gershenson (AAG) stated that we [2] "found that 'zero-point fluctuations of electrons' contribute to the dephasing rate 1͞t w ." We made no such claims. Obviously, the eigenmodes of any quantum system preserve their coherence. On the other hand, single-particle properties of an interacting system-which are not directly expressed in terms of eigenmodes-can display a finite decoherence length L w even in the lowtemperature limit. An example is provided by a particle coupled to a harmonic oscillator bath [4], which we discuss explicitly below. This is also the case for the weak localization correction to the conductivity ds in the presence of interaction, where we found [2] L w to remain finite at T ! 0. AAG furthermore concluded that our procedure is "simply wrong" because "some contributions were lost." This is not the case, as demonstrated by the fact that our approach [2]-if analyzed perturbativelyreproduces the AAG result for ds (Ref.[2] of [1]) before disorder averaging. The main discrepancy between [1] and [2] is due to the golden rule approximation employed by AAG and not due to averaging over disorder.

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