Title: BCS Critical Temperature on Half-Spaces Show Chinese title

Title: 半空间上的BCS临界温度

Abstract: We study the BCS critical temperature on half-spaces in dimensions $d=1,2,3$ with Dirichlet or Neumann boundary conditions. We prove that the critical temperature on a half-space is strictly higher than on $\mathbb{R}^d$, at least at weak coupling in $d=1,2$ and weak coupling and small chemical potential in $d=3$. Furthermore, we show that the relative shift in critical temperature vanishes in the weak coupling limit. Show Chinese abstract

Abstract: 我们研究了维度为$d=1,2,3$的半空间上的 BCS 临界温度，分别考虑了狄利克雷和诺依曼边界条件。 我们证明了在半空间上的临界温度严格高于在$\mathbb{R}^d$上的临界温度，至少在$d=1,2$中弱耦合以及在$d=3$中弱耦合且小化学势时成立。 此外，我们还表明临界温度的相对变化在弱耦合极限下趋于零。