论文标题
MIT袋模型在无限圆锥上的自我相关性
Self-adjointness for the MIT bag model on an unbounded cone
论文作者
论文摘要
我们认为在无限的三维圆锥上，无质量的零零操作员带有MIT袋边界条件。对于凸锥，我们证明该操作员是在四组分$ h^1 $上定义的自动偶会 - 功能满足MIT袋边界条件。该结果的证明依赖于变量的分离和一维光纤式型操作员的光谱估计值。此外，我们还为非凸锥的同一域上的自相关性提供了数值证据。此外，对于凸锥上的这种狄拉克操作员来说，我们证明了这种耐心的不平等，尤其是通过一类无限势能在扰动下产生自我接触性的稳定性。还讨论了我们的结果的进一步扩展到具有量子点边界条件的DIRAC操作员。
We consider the massless Dirac operator with the MIT bag boundary conditions on an unbounded three-dimensional circular cone. For convex cones, we prove that this operator is self-adjoint defined on four-component $H^1$--functions satisfying the MIT bag boundary conditions. The proof of this result relies on separation of variables and spectral estimates for one-dimensional fiber Dirac-type operators. Furthermore, we provide a numerical evidence for the self-adjointness on the same domain also for non-convex cones. Moreover, we prove a Hardy-type inequality for such a Dirac operator on convex cones, which, in particular, yields stability of self-adjointness under perturbations by a class of unbounded potentials. Further extensions of our results to Dirac operators with quantum dot boundary conditions are also discussed.
