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Zeta functions in the interaction of light and matterDiscovering the mathematics of quantum Rabi models 
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The study of the interaction between light and matter is fundamental for high impact applications in quantum information science including the realization of quantum computers. In this research, to understand the spectral zeta function of the quantum Rabi model (QRM), one of the most basic models describing interaction of light and matter, we devised a completely new method for the computation of explicit formula of the heat kernel of the QRM. This new method avoids the use of (continuous) path integrals by using a combination of techniques from several areas of mathematics, including combinatorics and representation theory. In addition to the study of the spectral zeta function and its related arithmetics, the resulting formula gives new insights into the physics of quantum interaction and is expected to have many new applications.
[1] C. Reyes-Bustos, M. Wakayama, “The heat kernel for the quantum Rabi model”, Adv. Theor. Math. Phys., Vol. 26, No. 5, pp. 1347-1447, 2022.
[2] C. Reyes-Bustos, M. Wakayama, “Heat kernel for the quantum Rabi model: II. Propagators and spectral determinants”, J. Phys. A: Math. Theor. , Vol. 54, 115202, 2021.
Cid Reyes Bustos
Institute for Fundamental Mathematics