Quantum stability and screening in superconducting metallic weak links

Approximation methods are developed for solving the time-dependent Bogoliubov—de Gennes equations for inhomogeneous superconducting systems with electromagnetic fields and thermal fluctuations. Space and time variations of the pair potential's phase in weak links are transformed into the appropriate vector and scalar potentials which are handled perturbation theoretically. In this way we compute quasiparticle scattering in superconducting-normal-superconducting junctions due to the random voltage of Nyquist-Johnson noise and obtain a microscopic criterion for the destruction of phase coherence between the $S$ layers. Considering the problem of size quantization of Andreev states bound in the N region, we show that, at sufficiently high temperatures, a great number of them survive the destruction of phase coherence by thermal fluctuations. The first step of an iteration process which uses the gauge-invariant phase difference in Bardeen and Johnson's Josephson current allows an estimate of the amount of screening of magnetic fields by Josephson currents.