论文标题
二维稀释的玻色气体的自由能。 ii。上限
The free energy of the two-dimensional dilute Bose gas. II. Upper bound
论文作者
论文摘要
我们证明了在热力学极限下的二维均匀bose气体的自由能的上限。我们表明，对于$ a^2ρ\ ll 1 $和$βρ\ gtrsim 1 $单位容量的自由能量与非相互作用的系统不同，最多最多$4πρ^2 | \ ln a^2ρ|^2ρ|^{ - 1}（2 - [1-β_ {1-β_ {1-β_ {c} c} $ a $是两体相互作用潜力的散射长度，$ρ$是密度，$β$，反向温度，$β_ {\ mathrm {c}} $是逆Berezinskii - Kosterlitz- kosterlitz--对于超富度的无数关键温度。结合相应的匹配下限在\ cite {dms19}中证明，这在渐近扩展中表现出相等性。
We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for $a^2 ρ\ll 1$ and $βρ\gtrsim 1$ the free energy per unit volume differs from the one of the non-interacting system by at most $4 πρ^2 |\ln a^2 ρ|^{-1} (2 - [1 - β_{\mathrm{c}}/β]_+^2)$ to leading order, where $a$ is the scattering length of the two-body interaction potential, $ρ$ is the density, $β$ the inverse temperature and $β_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved in \cite{DMS19} this shows equality in the asymptotic expansion.
