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The Bogoliubov Free Energy Functional II: The Dilute Limit.
- Source :
- Communications in Mathematical Physics; May2018, Vol. 360 Issue 1, p347-403, 57p
- Publication Year :
- 2018
-
Abstract
- 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 ∫V→8πa<inline-graphic></inline-graphic>, we determine the critical temperature to be Tc=Tfc(1+1.49ρ1/3a)<inline-graphic></inline-graphic> to leading order. Here, Tfc<inline-graphic></inline-graphic> is the critical temperature of the free Bose gas, <italic>ρ</italic> is the density of the gas and <italic>a</italic> is the scattering length of the pair-interaction potential <italic>V</italic>. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee-Huang-Yang formula in the limit ∫V→8πa<inline-graphic></inline-graphic>. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 360
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 129323069
- Full Text :
- https://doi.org/10.1007/s00220-017-3064-x