论文标题
磁性laplacian的痕量公式在零能级
Trace formula for the magnetic Laplacian at zero energy level
论文作者
论文摘要
该纸用于与紧凑型歧管上的磁性系统相关的磁性拉普拉斯的痕量公式。该公式是半经典gutzwiller痕量公式的自然概括，并在磁场形式精确的情况下还原。它与作者先前与I.A.的作品中研究的Guillemin-uribe Trace公式有所不同。泰米诺夫。此外，与这项工作相反，重点是零能级的痕量公式，这是一个关键的能级。本文概述了与零能级处的痕量公式相关的主要概念和结果，描述了其证明的各种方法，并给出了其计算的具体示例。此外，对Gutzwiller痕量公式进行了简要审查，以定期和临界能量水平。
The paper is devoted to the trace formula for the magnetic Laplacian associated with a magnetic system on a compact manifold. This formula is a natural generalization of the semiclassical Gutzwiller trace formula and reduces to it in the case when the magnetic field form is exact. It differs somewhat from the Guillemin-Uribe trace formula studied in the author's previous work with I.A. Taimanov. Moreover, in contrast to that work, the focus is on the trace formula at the zero energy level, which is a critical energy level. The paper gives an overview of the main notions and results related to the trace formula at the zero energy level, describes various approaches to its proof, and gives concrete examples of its computation. In addition, a brief review of the Gutzwiller trace formula for regular and critical energy levels is given.
