论文标题
特征值渐近学用于限制具有复杂电势的磁性schrödinger操作员
Eigenvalue asymptotics for confining magnetic Schrödinger operators with complex potentials
论文作者
论文摘要
本文致力于欧几里得平面上电磁施罗丁式操作员的光谱分析。在半经典极限中，我们得出了一个伪分别的有效操作员，该操作员使我们能够描述复杂平面的各种情况和适当区域的光谱。在拟议的统一框架中，不仅证明（或恢复）自我关节案例的结果，而且当电势值得评估时，建立了新的结果。在这种情况下，当非频道之间带有其特定问题（缺乏“光谱定理”，分辨率估计值）时，仍然准确描述了自助关节案例的“低层特征值”的类似物，并且频谱差距估计。
This article is devoted to the spectral analysis of the electro-magnetic Schrödinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum in various situations and appropriate regions of the complex plane. Not only results of the selfadjoint case are proved (or recovered) in the proposed unifying framework, but new results are established when the electric potential is complex-valued. In such situations, when the non-selfadjointness comes with its specific issues (lack of a "spectral theorem", resolvent estimates), the analogue of the "low-lying eigenvalues" of the selfadjoint case are still accurately described and the spectral gaps estimated.
