10.1007/s00220-017-3064-x
Napiórkowski, Marcin M
Marcin M
Napiórkowski
Reuvers, Robin
Robin
Reuvers
Solovej, Jan
Jan
Solovej
The Bogoliubov free energy functional II: The dilute Limit
Springer
2018
2018-12-11T11:47:09Z
2020-01-21T13:20:51Z
journal_article
/record/554
/record/554.json
00103616
1511.05953
We analyse the canonical Bogoliubov free energy functional in three dimensions at low temperatures in the dilute limit. We prove existence of a first-order phase transition and, in the limit (Formula presented.), we determine the critical temperature to be (Formula presented.) to leading order. Here, (Formula presented.) is the critical temperature of the free Bose gas, ρ is the density of the gas and a is the scattering length of the pair-interaction potential V. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula in the limit (Formula presented.).