论文标题
在强磁场中的狄拉克袋模型上
On the Dirac bag model in strong magnetic fields
论文作者
论文摘要
在这项工作中，我们研究了二维域上的狄拉克操作员，该结构域耦合到垂直于平面的磁场。我们专注于无限质量边界条件（也称为MIT袋条件）。 在有界结构域的情况下，我们在强磁场的极限下建立了低洼（正和负）能量的渐近行为。此外，对于一个恒定的磁场$ b $，我们在半平面上研究了问题，发现狄拉克操作员具有连续的频谱，除了大小$ a \ _0 \ sqrt {b} $的间隙，其中$ a \ _0 \ in（0，\ sqrt {2}）$是通用的常数。值得注意的是，这个常数也表征了系统中系统的某些能量。 我们讨论了这些发现以及以前的工作如何对在一般边界条件下的磁性二维操作员的特征值渐近学给出相当完整的描述。
In this work we study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular to the plane. We focus on the infinite-mass boundary condition (also called MIT bag condition). In the case of bounded domains, we establish the asymptotic behavior of the low-lying (positive and negative) energies in the limit of strong magnetic field. Moreover, for a constant magnetic field $B$, we study the problem on the half-plane and find that the Dirac operator has continuous spectrum except for a gap of size $a\_0\sqrt{B}$, where $a\_0\in (0,\sqrt{2})$ is a universal constant. Remarkably, this constant characterizes certain energies of the system in a bounded domain as well. We discuss how these findings, together with our previous work, give a fairly complete description of the eigenvalue asymptotics of magnetic two-dimensional Dirac operators under general boundary conditions.
