标题： 拉普拉斯算子在常复磁场下的光谱的突然变化 显示英文标题

标题： Abrupt changes in the spectra of the Laplacian with constant complex magnetic field

摘要： 我们分析在平面中受齐次复磁场所作用的拉普拉斯算子的谱。 对于实磁场，众所周知，谱由无限重数的孤立本征值（朗道能级）组成。 我们证明当磁场具有非零虚部时，谱扩展以覆盖整个复平面。 此外，我们表明朗道能级（适当旋转并在复平面上嵌入）仍然存在，除非磁场均是纯虚数，在这种情况下它们消失，谱变为纯连续的。 显示英文摘要

摘要： We analyze the spectrum of the Laplace operator, subject to homogeneous complex magnetic fields in the plane. For real magnetic fields, it is well-known that the spectrum consists of isolated eigenvalues of infinite multiplicities (Landau levels). We demonstrate that when the magnetic field has a nonzero imaginary component, the spectrum expands to cover the entire complex plane. Additionally, we show that the Landau levels (appropriately rotated and now embedded in the complex plane) persists, unless the magnetic field is purely imaginary in which case they disappear and the spectrum becomes purely continuous.