TY - JOUR
T1 - The Bogoliubov free energy functional II
T2 - The dilute limit
AU - Napiórkowski, Marcin
AU - Reuvers, Robin
AU - Solovej, Jan Philip
PY - 2018/5/1
Y1 - 2018/5/1
N2 - 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→ 8 πa, we determine the critical temperature to be Tc= Tfc(1 + 1.49 ρ1 / 3a) to leading order. Here, Tfc 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 ∫ V→ 8 πa.
AB - 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→ 8 πa, we determine the critical temperature to be Tc= Tfc(1 + 1.49 ρ1 / 3a) to leading order. Here, Tfc 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 ∫ V→ 8 πa.
KW - math-ph
KW - math.MP
U2 - 10.1007/s00220-017-3064-x
DO - 10.1007/s00220-017-3064-x
M3 - Journal article
SN - 0010-3616
VL - 360
SP - 347
EP - 403
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -