AI 中文总结
本研究基于可积模型，通过ODE/IM公式建立围道积分，推导了厄米与PT对称振荡器的热配分函数及谱泽塔函数，搭建了量子谱函数与可积模型的直接关联。
AI 中文摘要
我们开发了一种基于ODE/IM的公式，用于计算均匀厄米振荡器和PT对称振荡器的热配分函数与谱泽塔函数。对于这两类系统，量子化条件可通过计数函数a(E)表示，该函数可通过可积模型的Destri-de Vega方程求解。随后我们将配分函数与谱泽塔函数表示为涉及计数函数的围道积分，从而在量子谱函数与可积模型之间建立了直接桥梁。
英文摘要
We develop an ODE/IM-based formulation for the thermal partition function and the spectral zeta function of the homogeneous Hermitian and PT-symmetric oscillators. For both classes of systems, the quantization condition can be expressed using the counting function $a(E)$, which can be solved via the Destri-de Vega equation of the integrable model. We then express the partition function and spectral zeta function as contour integrals involving the counting function, thereby providing a direct bridge between quantum spectral functions and integrable models.
Comments18 pages, 1 figures, 4 tables
