| Abstract: | At a junction between a normally conducting wire and a superconductor, electrons can join the condensate of the superconductor by emitting a hole (Andreev reflection) while exciting phase oscillations in the superconductor. The system is argued to be a microscopically solvable model for decoherence. I use an analogy to a classical system with noise, based on the picture that the charge entering the superconductor is analogous to thermal noise with distribution determined by its initial wave function. Following similar ideas to those used in the classical theory of a system in contact with a bath, I derive a path integral for the evolution of the density matrix of the superconductor, showing that there is a quantized friction. I use it to derive the steady state density matrix for various initial states of the normal metal, and show that in some cases the superconductor develops a thermal steady state, while in other situations different modes have different effective temperatures. |