reyes [at] c.titech.ac.jp

# Cid Reyes Bustos

Mathematician

## Publications

### Preprints

Comments are welcome!

- 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

### 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*.

- This is a digest presentation of
- 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*.

- Please note that the contents of this research report are superseded by

### 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.

- This is the basis for the article
- 2015
*Cayley-type graphs for group-subgroup pairs*. Master thesis. Kyushu University. Download pdf.- The basis for the article
*Cayley-type graphs for group-subgroup pairs*.

- The basis for the article
- 2010
- Braid-group cryptrography (in Spanish). Bachelor thesis. Download here.
- An overview of several cryptosystems based on braid groups and their cryptanalysis. The design of a python implementation is also included.