2013/06/20 by Levent Akant, Emine Ertuğrul, Akant, Levent +6
Mathematics · Physics and Astronomy · #35K08 #51P05 #82B10 #Cosmology and Gravitation Theories #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #High Energy Physics - Theory (hep-th) #High-Energy Particle Collisions Research #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP #msc:35K08 #msc:51P05 #msc:82B10
paper · pdf · doi:10.48550/arxiv.1306.4839
34 pages, new results and some references are added, no figures
openalex publication_date 2013/06/20 · arxiv created 2014/03/28 · arxiv updated 2014/03/31 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with nonnegative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The main focus is on the nonrelativistic gas. However, special relativistic ideal gas is also discussed. The thermodynamic limit of the heat kernel and eigenvalue estimates is taken and the results are used to derive bounds for the depletion coefficient. In the case of a weakly interacting gas Bogoliubov approximation is employed. The ground state is analyzed using heat kernel methods and finite size effects on the ground state energy are proposed. The justification of the c-number substitution on a manifold is given.