Number Theoretic Study in Quantum Interactions

The quantum interaction models, with the quantum Rabi model as a distinguished representative, are recently appearing ubiquitously in various quantum systems including cavity and circuit quantum electrodynamics, quantum dots and artificial atoms, with potential applications in quantum information technologies including quantum cryptography and quantum computing (Haroche and Raimond 2008; Yoshihara et al. 2018). In this extended abstract, based on the contents of the talk at the conference, we describe shortly certain number theoretical aspects arising from thenon-commutative harmonic oscillators (NCHO: see Parmeggiani and Wakayama 2001; Parmeggiani 2010) and quantum Rabi model (QRM: see Braak 2011 for the integrability) through their respective spectral zeta functions.