What are the implications of a phase gradient Vo(a), e.g. the phase at one end of a super- conducting sample (L) is different to the other end o(R)? The superconducting order parameter is single-valued, implying that V(x e) = v(x+e) as 0. What is the corresponding condition on the superconducting phase (x)? Considering the bulk of a supercoducting ring, explain why: "change in o around the ring = flux through the loop", which (after including constants) translates to = c Are = n =n. = (Here A change in o around the ring).