Fermion Clustering in an Exactly-Soluble N-Fermion Model for Hadronic, Nuclear and Superconductivity Physics
We highlight the dynamical similarities between quark interactions, effective nucleon-nucleon interactions and the 3D electron fluid “jellium” model, on the one hand, and the exactly-soluble 1D fermion fluid with attractive delta-fuction pairwise potentials, on the other. The latter model is characterized by clustering of particles at low density and strong coupling. This motivates solving the Cooper pair problem within the model for all couplings and/or densities, a task accomplished exactly in graphical form. For weak coupling the essential singularity characteristic of standard 3D low-temperature superconductivity emerges, while for strong coupling BCS theory reproduces that exact ground-state system energy. The transition from large-coherence-length (low-T c-like) Cooper pairs to small (“bipolaron”, high-T c-like) ones is smooth.
KeywordsNuclear Matter Essential Singularity Full Curf Delta Potential Fermion Fluid
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