The Bogoliubov free energy functional II: The dilute Limit Journal Article


Author(s): Napiórkowski, Marcin; Reuvers, Robin; Solovej, Jan P
Article Title: The Bogoliubov free energy functional II: The dilute Limit
Affiliation IST Austria
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 (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.).
Journal Title: Communications in Mathematical Physics
Publisher: Elsevier  
Date Published: 2017-12-18
Start Page: Epub ahead of print
URL:
DOI: 10.1007/s00220-017-3064-x
Open access: yes (repository)