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

Title: BCS临界温度在半空间上

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: 我们研究在维度$d=1,2,3$的半空间上BCS临界温度，具有狄利克雷或诺伊曼边界条件。 我们证明，在弱耦合情况下，半空间上的临界温度严格高于$\mathbb{R}^d$上的临界温度，至少在$d=1,2$中是如此，并且在$d=3$的弱耦合和小化学势情况下也是如此。 此外，我们表明，在弱耦合极限下，临界温度的相对变化趋于零。