ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
As a microscopic description of the Josephson junction, two BCS models, are studied in the strict pair formulation with quite an arbitrary weak coupling potential. The modular formalism, the separate gauge transformations, and the limiting dynamics are analyzed for the interacting system in terms of the GNS representation of the uncoupled limiting Gibbs state. By means of the Connes theory the condensed Cooper pair and the quasiparticle spectrum is shown to be stable against weak perturbations. The modular formalism is used to construct a local approximation to the renormalized particle number operator and, by this, its time dependence, in spite of this observable not being affiliated with the von Neumann algebra of the temperature representation. The time derivation from this unbounded operator-valued function coincides with the limit of the local currents and splits under a natural assumption into a sum of the Josephson and the quasiparticle current operator extending the two-fluid picture also to the coupled model.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527152
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