 1939 J.B. Bru and W. de Siqueira Pedra
 Macroscopic LongRange Dynamics of Fermions and Quantum Spins on the Lattice  An Introduction
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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 quantumspin systems with longrange, or meanfield, interactions. In particular, they show that longrange dynamics in infinite volume are equivalent to intricate combinations of classical and quantum shortrange dynamics, opening new theoretical perspectives, as explained in [1]. This phenomenon is a direct consequence of the highly nonlocal character of longrange, or meanfield, 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 strongcoupling BCSHubbard model. The dynamical properties of this model are technically easy to study, albeit nontrivial, 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 (swave) superconductivity, in the strongcoupling approximation. Its behavior at thermodynamical equilibrium was rigorously known, but not its infinitevolume dynamics.
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