描述石墨烯量子点的Dirac算符的谱隙
Spectral gaps of Dirac operators describing graphene quantum dots
摘要：
二维狄拉克算符描述了石墨烯中的低能激发。不同的边界条件的选择会导致所得到的算子的谱的质的差异。对于一个家庭的边界条件，我们发现一个下界的频谱间隙约为零，成比例的$|Ω|^{-1/2}$，其中$Ω\subset \mathbb{R}^2$是有界区域的狄拉克运营商的行为。这个家族包含了物理学文献中用于描述石墨烯量子点的所谓无限质量和扶手椅案例。
英文摘要：
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary conditions, we find a lower bound to the spectral gap around zero, proportional to $|Ω|^{-1/2}$, where $Ω\subset \mathbb{R}^2$ is the bounded region where the Dirac operator acts. This family contains the so-called infinite mass and armchair cases used in the physics literature for the description of graphene quantum dots.
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