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
Y1 - 2018
N2 - We analyse the canonical Bogoliubov free energy functional at low temperatures in the dilute limit. We prove existence of a first order phase transition and, in the limit $a_0\to a$, we determine the critical temperature to be $T_{\rm{c}}=T_{\rm{fc}}(1+1.49(\rho^{1/3}a))$ to leading order. Here, $T_{\rm{fc}}$ is the critical temperature of the free Bose gas, $\rho$ is the density of the gas, $a$ is the scattering length of the pair-interaction potential $V$, and $a_0=(8\pi)^{-1}\widehat{V}(0)$ its first order approximation. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee-Huang-Yang formula in the limit $a_0\to a$.
AB - We analyse the canonical Bogoliubov free energy functional at low temperatures in the dilute limit. We prove existence of a first order phase transition and, in the limit $a_0\to a$, we determine the critical temperature to be $T_{\rm{c}}=T_{\rm{fc}}(1+1.49(\rho^{1/3}a))$ to leading order. Here, $T_{\rm{fc}}$ is the critical temperature of the free Bose gas, $\rho$ is the density of the gas, $a$ is the scattering length of the pair-interaction potential $V$, and $a_0=(8\pi)^{-1}\widehat{V}(0)$ its first order approximation. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee-Huang-Yang formula in the limit $a_0\to a$.
KW - math-ph
KW - math.MP
U2 - 10.1007/s00220-017-3064-x
DO - 10.1007/s00220-017-3064-x
M3 - Journal article
VL - 360
SP - 347
EP - 403
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -