Abstract
In the second lesson, we first discussed a subtle dissipative mechanism that can affect Josephson junctions in a non-equilibrium situation, which is the parity defect of superconducting electrodes. If an insulated junction has an odd number of electrons, one electron will remain single and may be accelerated if a voltage arises between the two electrodes. We then devoted the rest of the lesson to the problem of the nature of the conjugate variable of the flux through the Josephson element. This problem is simplified in two extreme cases. If at least one of the junction's electrodes is electrically insulated, the conjugate variable of the flux is the total charge of this electrode, a discrete variable which is a multiple of the charge of a Cooper pair. If, on the other hand, the junction is shunted by a pure inductance, the conjugate flux variable is the DC charge stored in the junction capacitance. Note that while in the first case, the wave function associated with the flux is periodic, with a period equal to the superconducting flux quantum, in the second case, the wave function extends along the entire real number axis without any particular symmetry. In the case of a general electromagnetic environment for the junction, this " observes " the flux of the latter, and we are led to the problem of writing the Hamiltonian of an arbitrary quantum circuit dealt with in the 2008 lecture.
