Quantum coherence in systems with electron correlations will be studied by means of Green
functions, renormalized many-body theory, and numerical simulations. We will extend an
approximation earlier developed by us with a two-particle self-consistency from the reduced
parquet equations qualitatively correctly describing the Kondo strong-coupling limit of the
metallic dot. The general theory will be applied to a model of quantum dot attached to
superconducting leads with the aim to explain and understand its behavior at the transition from
the spin singlet to the spin doublet state (zero-pi transition). The dot will be studied in an applied weak magnetic field in order to understand this transition and the properties of the spin doublet state with a degenerate ground state. The magnetic solution in a consistent theory must continuously match the non-magnetic one in the limit of the vanishing field. We further extend the static approximation from the reduced parquet equations to a dynamical one to make it applicable to low-dimensional lattice systems with long-range quantum coherence.
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