19-39 J.-B. Bru and W. de Siqueira Pedra
Macroscopic Long-Range Dynamics of Fermions and Quantum Spins on the Lattice - An Introduction (304K, pdf) Jun 14, 19
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Abstract. The aim of the current paper is to present, in a concise way, our recent, very general, mathematically rigorous studies [1,2] on the dynamical properties of fermions and quantum-spin systems with long-range, or mean-field, interactions. In particular, they show that long-range dynamics in infinite volume are equivalent to intricate combinations of classical and quantum short-range dynamics, opening new theoretical perspectives, as explained in [1]. This phenomenon is a direct consequence of the highly non-local character of long-range, or mean-field, interactions. Note that [1,2,3] are altogether about 200 pages long. Therefore, as a simple example allowing to emphasize the key points of [1,2], we consider here the strong-coupling BCS-Hubbard model. The dynamical properties of this model are technically easy to study, albeit non-trivial, and this example is thus very pedagogical. From the physical point of view, this model is also interesting because it highlights the possible thermodynamic impact of the (screened) Coulomb repulsion on (s-wave) superconductivity, in the strong-coupling approximation. Its behavior at thermodynamical equilibrium was rigorously known, but not its infinite-volume dynamics.

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