Quantum statistical mechanics for superstable interactions: Bose-Einstein statistics

R. Esposito, Francesco Nicoló, Mario Pulvirenti

Peter Bongaarts

J. Lauwers, André F. Verbeure, Valentin Anatol'evich Zagrebnov

Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose–Einstein condensation for such interacting systems.

Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran +2 more

Identical systems, or entities, are indistinguishable in quantum mechanics (QM), and the symmetrization postulate rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis on the historical development of QM attributes the origin of quantum statistics, in particular, Bose-Einstein statistics, to a lack of statistical independence of the micro-states of identical quantum entities. We have recently identified Bose-Einstein statistics in the combination of words in large texts, as a consequence of the entanglement created by the meaning carried by words when they combine in human language. Relying on this investigation, we put forward the hypothesis that entanglement, hence the lack of statistical independence, is due to a mechanism of contextual updating, which provides deeper reasons for the appearance of Bose-Einstein statistics in human language. However, this investigation also contributes to a better understanding of the origin of quantum mechanical statistics in physics. Finally, we provide new insights into the intrinsically random behaviour of microscopic entities that is generally assumed within classical statistical mechanics.

Uduzei F. Edgal, David L. Huber

Joseph V. Pulé, André F. Verbeure, Valentin Anatol'evich Zagrebnov

We prove, in great generality, that in a system of bosons, whenever Bose condensation in a nonzero mode occurs then there is also spontaneous breaking of translation symmetry. In particular the proof holds for realistic Bose systems with two-body superstable interaction. This generalizes an old result proving that the occurrence of Bose-Einstein condensation in the zero mode implies spontaneous breaking of gauge invariance.