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No-cooperative Equilibria of Spin and Fermi Systems With Long Range Interactions

Walter de Siqueira Pedra
(Mainz)
Analyseseminar
Mandag, 13 august, 2012, at 15:15-16:00, in Aud. D3 (1531-215)
Abstrakt:
In a joint work with Jean-Bernard Bru, we define a Banach space M1 of models for fermions or quantum spins in the lattice with long-range interactions and make explicit the structure of equilibrium states of any model in M1. In particular, we give 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. Depending on the model, our method provides a systematic way to study all its correlation functions and can thus be used to analyze the physics of long range interactions. Furthermore, we show that the thermodynamics of long range models is governed by the non-cooperative equilibria of a zero-sum game, called here thermodynamic game.
Kontaktperson: Bent Ørsted