Majorana台球基态的费米子宇称开关
Fermion-parity switches of the ground state of Majorana billiards
摘要：
马约拉纳台球是一个大小不一、形状任意的超导岛，承载着马约拉纳束缚态。研究了马约拉纳台球基态的费米子宇称开关。特别地，我们研究了这些费米子宇称开关的密度和统计作为施加磁场和化学势的函数。我们推导出公式，说明如何费米子宇称开关的平均密度取决于几何形状的台球。此外，我们展示了如何围绕这个平均值的振荡是由经典的周期轨道的台球。最后，我们发现，这些费米子奇偶开关的间距的统计是普遍的，并描述了一个随机矩阵系综，其中的选择取决于在其正常状态下的系统的反对酉对称性。因此，我们证明，“一个可以听到（信息）的形状马约拉纳台球”通过调查其“费米子宇称开关谱”。
英文摘要：
Majorana billiards are finitely sized, arbitrarily shaped superconducting islands that host Majorana bound states. We study the fermion-parity switches of the ground state of Majorana billiards. In particular, we study the density and statistics of these fermion-parity switches as a function of applied magnetic field and chemical potential. We derive formulae that specify how the average density of fermion-parity switches depends on the geometrical shape the billiard. Moreover, we show how oscillations around this average value is determined by the classical periodic orbits of the billiard. Finally, we find that the statistics of the spacings of these fermion-parity switches are universal and are described by a random matrix ensemble, the choice of which depends on the antiunitary symmetries of the system in its normal state. We thus demonstrate that "one can hear (information about) the shape of a Majorana billiard" by investigating its "fermion-parity switch spectrum".
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