Non-cooperative Equilibria of Fermi Systems With Long Range Interactions.
Jean Bernard Bru,
Ikerbasque, Depto Matemáticas UPV/EHU
Jueves 10 de diciembre 2009
Following the work of Araki and Moriya about the mathematics of
equilibrium states of fermion lattice systems with local interactions,
with W. de Siqueira Pedra, we define a Banach space of Fermi models
including also long range interactions, and explicit the structure of
equilibrium states for such models. This gives a first answer to an old
open problem in mathematical physics - first addressed by Ginibre in 1968
within a different context - about the validity of the so-called
Bogoliubov approximation on the level of states. The final result has a
direct interpretation in term of a two-person zero-sum game and it can
provide a systematic way to study all correlation functions. Therefore
this result can be used to analyze the physics of long range interactions.