On ergodic states, spontaneous symmetry breaking and the Bogoliubov quasi-averages

Walter F. Wreszinski (1) , Valentin Zagrebnov (2)

1 Departamento de Fisica Matematica
2 I2M - Institut de Mathématiques de Marseille

It is shown that Bogoliubov quasi-averages select the pure or ergodic states in the ergodic decomposition of the thermal (Gibbs) state. Our examples include quantum spin systems and many-body boson systems. As a consequence, we elucidate the problem of equivalence between Bose-Einstein condensation and the quasi-average spontaneous symmetry breaking (SSB) discussed for continuous boson systems. The multi-mode extended van den Berg-Lewis-Pul\'{e} condensation of type III demonstrates that the only physically reliable quantities are those that defined by Bogoliubov quasi-averages.

Domaines: Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]

Walter F. Wreszinski, Valentin Zagrebnov. On ergodic states, spontaneous symmetry breaking and the Bogoliubov quasi-averages. 2016. ⟨hal-01342904⟩