The Bogoliubov free energy functional II. The dilute limit

摘要: We analyse the canonical Bogoliubov free energy functional at low temperatures in dilute limit. prove existence of a first order phase transition and, limit $a_0\to a$, we determine critical temperature to be $T_{\rm{c}}=T_{\rm{fc}}(1+1.49(\rho^{1/3}a))$ leading order. Here, $T_{\rm{fc}}$ is Bose gas, $\rho$ density $a$ scattering length pair-interaction potential $V$, and $a_0=(8\pi)^{-1}\widehat{V}(0)$ its approximation. also asymptotic expansions for energy. In particular, recover Lee-Huang-Yang formula a$.