The Bogoliubov free energy functional II: The dilute limit
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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 $a_0\to a$.
Original language | English |
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Journal | Communications in Mathematical Physics |
Volume | 360 |
Issue number | 1 |
Pages (from-to) | 347–403 |
Number of pages | 57 |
ISSN | 0010-3616 |
DOIs | |
Publication status | Published - 2018 |
- math-ph, math.MP
Research areas
Links
- https://arxiv.org/pdf/1511.05953
Accepted author manuscript
ID: 190447955