PHASE-DEPENDENT MAGNETOCONDUCTANCE FLUCTUATIONS IN A CHAOTIC JOSEPHSON-JUNCTION

Motivated by recent experiments by Den Hartog et al., we present a ran dom-matrix theory for the magnetoconductance fluctuations of a chaotic quantum dot that is coupled by point contacts to two superconductors and one or two normal metals. There are aperiodic conductance fluctuat ions as a function of the magnetic field through the quantum dot and 2 pi-periodic fluctuations as a function of the phase difference phi of the superconductors. If the coupling to the superconductors is weak c ompared to the coupling to the normal metals, the phi dependence of th e conductance is harmonic, as observed in the experiment. In the oppos ite regime, the conductance becomes a random 2 pi-periodic function of phi, in agreement with the theory of Altshuler and Spivak. The theore tical method employs an extension of the circular ensemble which can d escribe the magnetic-field dependence of the scattering matrix.