Fiber decomposition of non-commutative harmonic oscillators by two-photon quantum Rabi models

The non-commutative harmonic oscillators (NcHO) and 2p-quantum Rabi models (2pQRM) are extensions of harmonic oscillators. The purpose of this paper is to give a relationship between NcHO and 2pQRM, and the fiber decomposition of NcHO by 2pQRM is shown. We also construct Feynman-Kac formulas of NcHO and 2pQRM. Then asymptotic behaviors of the spectral zeta function of 2pQRM is considered.