%0 Unpublished work
%T On ergodic states, spontaneous symmetry breaking and the Bogoliubov quasi-averages
%+ Departamento de Fisica Matematica
%+ Institut de Mathématiques de Marseille (I2M)
%A Wreszinski, Walter F.
%A Zagrebnov, Valentin
%Z Some of the issues dealt with in this paper originate in the open problem posed in Sec.3 of [SW09] and at the of [JaZ10]. One of us (W.F.W.) would like to thank G. L. Sewell for sharing with him his views on ODLRO along several years. He would also like to thank the organisers of the Satellite conference ”Operator Algebras and Quantum Physics” of the XVIII conference of the IAMP (Santiago de Chile) in Sao Paulo, July 17th-23rd 2015, for the opportunity to present a talk in which some of the ideas of the present paper were discussed. We are thankful to Bruno Nachtergaele for very useful remarks, suggestions, and corrections, which greatly improved and clarified the paper.
%8 2016-07-07
%D 2016
%Z 1607.03024
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Functional Analysis [math.FA]Preprints, Working Papers, ...
%X 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.
%G English
%2 https://hal.science/hal-01342904/document
%2 https://hal.science/hal-01342904/file/WZjuillet2016.pdf
%L hal-01342904
%U https://hal.science/hal-01342904
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TDS-MACS