Partition Functions of Hermitian and PT-Symmetric Oscillators from Integrable Models

2026/08/06 by Hongfei Shu, Jingjing Yang
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #quant-ph

paper · pdf

18 pages, 1 figures, 4 tables

arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

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.

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