eFTC-211101
Particle-Hole Description of the Bogoliubov Dilute Bosonic Gas Model in Small (Finite) Systems |
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Author: Y. Leblanc (eFieldTheory.COM) Email: AbstractThe standard theory of Bose-Einstein condensation (BEC) assumes that most particles occupy the ground state of the system. This view is based on the Bose-Einstein distribution for bosons. But such a distribution is easily shown to be pathological, especially very near the ground state where its variance actually blows up. On the other hand, a careful derivation of the boson distribution for finite systems yields a new and perfectly well behaved generic form compatible with a bosonic particle-hole description of the system. Reviewing the zero temperature canonical transformation theory to particles and holes for such a generic distribution, we succesfully apply it to the Bogoliubov theory of the dilute (weakly interacting) bosonic gas, a well known theoretical model of quantum liquids and superfluidity. We recover Bogoliubov's results without invoking Bose-Einstein condensation. Therefore, similarly to the case of the ideal gas, we find that the BEC description is replaced by a bosonic particle-hole description in the fully interacting case. We also describe the emergence of a new exclusion principle for finite systems which we call the Pauli-Bose exclusion principle. Copyright © 2021 Yvan Leblanc. All rights reserved
PACS: 05.30.Ch, 03.70.+k, 11.10.Gh Cite as: Leblanc, Y., "Particle-Hole Description of the Bogoliubov Dilute Bosonic Gas Model in Small (Finite) Systems", manuscript no. eFTC-211101 (2021). http://www.efieldtheory.com/abs/?eFTC-211101; doi:10.13140/RG.2.2.26730.44488. |
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