The Bogoliubov free energy functional II: The dilute limit

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 -