reyes [at] c.titech.ac.jp

# Cid Reyes Bustos

Mathematician

## Publications

### Preprints

2022
Covering models of the asymmetric quantum Rabi model: η-shifted non-commutative harmonic oscillators with Masato Wakayama. Preprint 2022. arXiv:2209.14665.
2020
The heat kernel of the asymmetric quantum Rabi model. Preprint 2020. arxiv:2012.13595

### Published articles and book chapters

2022
Heat kernel for the quantum Rabi model with Masato Wakayama. Adv. Theor. Math. Phys. 26 (5), 2022. In print. Preprint: arxiv:1906.09597.
2022
Degeneracy and hidden symmetry for the asymmetric quantum Rabi model with integral bias with Masato Wakayama. Commun. Number Theory Phys. 17 (3) 615-672, 2022. doi:10.4310/CNTP.2022.v16.n3.a4.
2021
Remarks on the hidden symmetry of the asymmetric quantum Rabi model with Daniel Braak and Masato Wakayama. J. Phys. A: Math. Theor. 54 285202, 2021. doi:10.1088/1751-8121/ac0508. Preprint 2021 arxiv:2101.04305
2021
Heat kernel for the quantum Rabi model II: propagators and spectral determinants with Masato Wakayama. J. Phys. A: Math. Theor. 54 115202, 2021. doi:10.1088/1751-8121/abdca7. Preprint 2020. arXiv:2008.05354
2020
Extended divisibility relations for constraint polynomials of the asymmetric quantum Rabi model in "International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC 2019)" eds. T. Takagi et al. doi:10.1007/978-981-15-5191-8_13
2018
Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model with Masato Wakayama and Kazufumi Kimoto. International Mathematics Research Notices, Volume 2021, Issue 12 (2021), 9458–9544. Published Online April 2020. doi:10.1093/imrn/rnaa034. Preprint version arxiv:1712.04152.
2017
Spectral degeneracies in the asymmetric quantum Rabi model with Masato Wakayama. in "Mathematical Modelling for Next- Generation Cryptography" eds. T. Takagi et al., Mathematics for Industry, Springer, 2017. doi: 10.1007/978-981-10-5065-7 7
2016
Cayley-type graphs for group-subgroup pairs. Linear Algebra and its Appplications. Volume 488 (2016), pages 320-349. doi: 10.1016/j.laa.2015.09.049
• An accepted manuscript version is available here. The Mathematica source code for the figure files is available here.

### Non-refereed publications

2019
Degeneracy structure of the spectrum of the asymmetric quantum Rabi model. RIMS Kôkyûroku 2123 (2019). Mathematical aspects of quantum fields and related topics.
• This is a digest presentation of Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model.
2018
Orthogonal polynomials related to the asymmetric quantum Rabi model. Proceedings of the Symposium on Representation Theory 2018 年度表現論シンポジウム講演集. doi.org/10.34508/repsympo.2018.0_121.
2014
Group-subgroup pair graphs. RIMS Kôkyûroku 1925 (2014). New Developments of Representation Theory and Harmonic Analysis. Research Institute for Mathematical Science. Kyoto University.
• Please note that the contents of this research report are superseded by Cayley-type graphs for group-subgroup pairs.

### Notes and other

2019
A simple continued fraction expansion for $$e^n$$. Preprint 2019. arxiv:1909.13597

### Theses

2018
Study on the spectrum of the asymmetric quantum Rabi model. Doctoral dissertation. Kyushu University. Download from here.
• This is the basis for the article Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model. The historical background and introduction to the study of the spectrum of the quantum Rabi model Hamiltonian may be useful.
2015