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arXiv · 2602.01628

Special values of spectral zeta functions of one-, two-photon quantum Rabi models and non-commutative harmonic oscillators

Ryosuke Nakahama
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Abstract

We find explicit expressions of the special values of the Hurwitz-type spectral zeta function $\zeta(\mathrm{H};n,\lambda)$ for the Hamiltonians $\mathrm{H}$ of the one-photon quantum Rabi model (1pQRM), the two-photon quantum Rabi model (2pQRM), and the non-commutative harmonic oscillator (NCHO), at positive integers $n$. Then the 1st term of the spectral zeta function of 1pQRM gives a generalization of Beukers' integral used for the proof of the irrationality of $\zeta(2)$ after Ap\'ery's work. A similar expression of the 1st term of that of 2pQRM is also discussed.

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Ryosuke Nakahama. 2026-02-02. Special values of spectral zeta functions of one-, two-photon quantum Rabi models and non-commutative harmonic oscillators. https://arxiv.org/abs/2602.01628

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