On Ergodic States, Spontaneous Symmetry Breaking and Quasi-Averages

Walter F. Wreszinski and Valentin A. Zagrebnov ()
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Walter F. Wreszinski: Instituto de Fisica USP
Valentin A. Zagrebnov: Centre de Mathématiques et Informatique - Technopôle Château-Gombert - 39

A chapter in Exploring Mathematical Analysis, Approximation Theory, and Optimization, 2023, pp 431-458 from Springer

Abstract: Abstract It is shown that the 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 of the gauge invariance recently discussed for continuous boson systems. The multi-mode extended van den Berg-Lewis-Pulé condensation of type III demonstrates that the only physically reliable quantities are those that defined by Bogoliubov quasi-averages.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-46487-4_17

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DOI: 10.1007/978-3-031-46487-4_17

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