开放系统拟正规和全传输模式的SUSY变换
SUSY Transformations for Quasinormal and Total-Transmission Modes of Open Systems
摘要：
准正规模是保守系统中正规模在开放系统中的对应物;由出射波边界条件定义，它们具有复特征值。研究了一个超对称（SUSY）系统具有相同的复准正模谱（或除一个本征值外相同）的条件。讨论自然也包括全传输模式（一个极端是输入，另一个极端是输出）。几种类型的超对称变换出现，每一个都用例子说明，包括不同的Poschl-Teller势之间的转换和众所周知的身份之间的两个宇称扇区的线性引力波传播的史瓦西背景的频谱。与正常模式的情况相反，可能存在多个基本上等谱的伙伴，每个都缺少不同的状态。超对称变换在双线性映射下保持正交性，这是保守系统通常的内积的模拟。超对称变换可以导致双重准正规和全透射模式，这一现象进行了分析和说明。超对称性伙伴的存在与否也与反演问题有关：开波系统是否唯一地由它们的复谱决定？
英文摘要：
Quasinormal modes are the counterparts in open systems of normal modes in conservative systems; defined by outgoing-wave boundary conditions, they have complex eigenvalues. The conditions are studied for a system to have a supersymmetric(SUSY) partner with the same complex quasinormal-mode spectrum (or the same except for one eigenvalue). The discussion naturally includes total-transmission modes as well(incoming at one extreme and outgoing at the other). Several types of SUSY transformations emerge, and each is illustrated with examples, including the transformation among different Poschl-Teller potentials and the well-known identity in spectrum between the two parity sectors of linearized gravitational waves propagating on a Schwarzschild background. In contrast to the case of normal modes, there may be multiple essentially isospectral partners, each missing a different state. The SUSY transformation preserves orthonormality under a bilinear map which is the analog of the usual inner product for conservative systems. SUSY transformations can lead to doubled quasinormal and total-transmission modes; this phenomenon is analysed and illustrated. The existence or otherwise of SUSY partners is also relevant to the question of inversion: are open wave systems uniquely determined by their complex spectra?
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