标题： 准正则模式与非自伴算子的解析延拓 显示英文标题

标题： Quasinormal modes and the analytical continuation of non-self-adjoint operators

摘要： 我们简要回顾了确定开放系统中准正规模（QNMs）及其相关频率的解析延拓方法。 我们基于Pöschl-Teller势探讨了两个完全可解的情形，以表明从量子力学中的束缚态问题出发，解析延拓方法无法确定特定问题的完整QNMs集合及其频率。 问题的根源在于，许多QNMs是那些不属于与之相关的Schrödinger算符自伴域的解的解析延拓结果，这挑战了该方法用于确定完整QNMs集合的应用性。 我们通过物理上相关的BTZ黑洞情形来说明这些问题，在此情形下，问题的自然定义域是负实轴。 显示英文摘要

摘要： We briefly review the analytical continuation method for determining quasinormal modes (QNMs) and the associated frequencies in open systems. We explore two exactly solvable cases based on the P\"oschl-Teller potential to show that the analytical continuation method cannot determine the full set of QNMs and frequencies of a given problem starting from the associated bound state problem in Quantum Mechanics. The root of the problem is that many QNMs are the analytically continued counterparts of solutions that do not belong to the domain where the associated Schr\"odinger operator is self-adjoint, challenging the application of the method for determining full sets of QNMs. We illustrate these problems through the physically relevant case of BTZ black holes, where the natural domain of the problem is the negative real line.