标题： 拓扑朗缪尔-回旋波 显示英文标题

标题： Topological Langmuir-cyclotron wave

摘要： 一个理论框架被开发出来，以描述拓扑朗缪尔-回旋波（TLCW），这是在磁化等离子体中最近识别出的一种拓扑表面激发态。作为一种拓扑波，TLCW在复杂边界上单向传播而不发生散射。TLCW被理论研究为不均匀等离子体中波的哈密顿量伪微分算子（PDO）$\hat{H}$的谱流。等离子体波的Weyl量子化的半经典参数被确定为电子回旋半径与系统不均匀尺度长度的比值。等离子体波的体哈密顿量符号H的厄米本征模束被形式地定义。由于经典连续介质中的动量空间通常可缩，因此动量空间上的本征模束的拓扑结构是平凡的。这与凝聚态物质形成鲜明对比。经典连续介质中本征模束的非平凡拓扑仅存在于相空间上。建立了一个边界同构定理，以促进在相空间中不可缩流形上的本征模束的陈数计算。它还定义了相空间中孤立Weyl点的拓扑电荷，而无需采用任何连接。利用这些代数拓扑技术以及Faure提出的指标定理，严格证明了朗缪尔波-回旋波共振处的Weyl点的非平凡拓扑生成了TLCW作为谱流。显示TLCW可以由相空间中的倾斜狄拉克锥准确建模。给出了通用倾斜相空间狄拉克锥的PDO整个谱的解析解，包括其谱流。倾斜狄拉克锥的谱流指标为一，其模式结构是一个平移高斯函数。 显示英文摘要

摘要： A theoretical framework is developed to describe the Topological Langmuir-Cyclotron Wave (TLCW), a recently identified topological surface excitation in magnetized plasmas. As a topological wave, the TLCW propagates unidirectionally without scattering in complex boundaries. The TLCW is studied theoretically as a spectral flow of the Hamiltonian Pseudo-Differential-Operator (PDO) $\hat{H}$ for waves in an inhomogeneous plasma. The semi-classical parameter of the Weyl quantization for plasma waves is identified to be the ratio between electron gyro-radius and the inhomogeneity scale length of the system. Hermitian eigenmode bundles of the bulk Hamiltonian symbol H for plasma waves are formally defined. Because momentum space in classical continuous media is contractible in general, the topology of the eigenmode bundles over momentum space is trivial. This is in stark contrast to condensed matters. Nontrivial topology of the eigenmode bundles in classical continuous media only exists over phase space. A boundary isomorphism theorem is established to facilitate the calculation of Chern numbers of eigenmode bundles over non-contractible manifolds in phase space. It also defines a topological charge of an isolated Weyl point in phase space without adopting any connection. Using these algebraic topological techniques and an index theorem formulated by Faure, it is rigorously proven that the nontrivial topology at the Weyl point of the Langmuir wave-cyclotron wave resonance generates the TLCW as a spectral flow. It is shown that the TLCW can be faithfully modeled by a tilted Dirac cone in phase space. An analytical solution of the entire spectrum of the PDO of a generic tilted phase space Dirac cone, including its spectral flow, is given. The spectral flow index of a tilted Dirac cone is one, and its mode structure is a shifted Gaussian function.