Condensed Cooper Pairs and Macroscopic Quantum Phenomena

  • Alfred Rieckers
Part of the NATO ASI Series book series (NSSB, volume 258)


We give in the first section an introduction into the basic notions of operator algebraic quantum theory with the emphasis on the state space of the quasi-local algebra. Representation theory and decomposition theory are related with the macroscopic distinguishability (disjointness) of states. In section 2 we use this formalism to discuss superconductivity in terms of a gauge covariant BCS-model in which the operators of the macroscopic phase and of the condensed Cooper pairs play a decisive role. Two weakly coupled BCS-superconductors constitute a model for the Josephson junction, in which the condensed Cooper pairs tunnel across the isolation barrier of the junction and provide one component of the two-fluid model. The Josephson relations are microscopically derived as operator equations.

In the last section the problem of a coherent superposition of two junction states which are macroscopically different (by having different phase differences), leads to an unconventional extension of the observable algebra to include the number operators which have been shown to be incompatible with the phase operators. In this extended framework the semi-phenomenological energy terms (connected with the capacitance and self-inductance) can be added to the previous junction Hamiltonian. We then have a rigorous formalism by means of which the actual discussions of macroscopic quantum phenomena can be reconsidered, clarified, and confirmed to a surprisingly large extent.


Density Operator Josephson Junction Coherent Superposition Cyclic Vector Superselection Rule 


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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Alfred Rieckers
    • 1
  1. 1.Institut für Theoretische PhysikTübingenGermany

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