math [at] cidrb . me

# Cid Reyes Bustos

Mathematician

## About me

I am a mathematician of the NTT Institute for Fundamental Mathematics at NTT Corporation.

My research interests are:

- Number theoretical aspects of quantum interaction models (quantum Rabi model and non-commutative harmonic oscillator)
- Graph theory, generalizations of Cayley graphs and harmonic analysis of graphs.
- Representation theory and orthogonal polynomials.
- Number theory, zeta functions and continued fractions.

## Affiliation

- Research Scientist. NTT Institute for Fundamental Mathematics, Communication Science Laboratories, NTT Corporation.
- Visiting Assistant Professor. School of Computing, Tokyo Institute of Technology.

My CV can be downloaded here. Last updated September 2024.

## News

**2024/09**The paper*Zeta limits for the spectrum of quantum Rabi models*was published in J. Math. Phys.**2024/09**Two expository articles were published in NTT Technical Review: Light-matter Interaction and Zeta Functions and Representation Theory and Combinatorics Arising from Determinants. Japane version (NTT技術ジャーナル) are 光と物質の相互作用とゼータ関数 and 行列式に始まる表現論と組合せ論.**2024/06**The paper*Spacing distribution for quantum Rabi models*was published in J. Phys. A: Math. Theor.**2024/06**I was awarded the*Grant-in-Aid for Early-Career Scientists*from JSPS for the period 2024-2026.**2023/09**The paper*The heat kernel of the asymmetric quantum Rabi model*was published in J. Phys. A: Math. Theor.**2023/08**The paper*Covering models of the asymmetric quantum Rabi model: η-shifted non-commutative harmonic oscillators*was published in Communications in Mathematical Physics. See here for a only-read version.

## Main Publications and preprints

Visit the publications page for the complete list of publications.

**2024.***Spacing distribution for quantum Rabi models*with**Linh Thi Hoai Nguyen, Daniel Braak and Masato Wakayama**. J. Phys. A: Math. Theor. Published Online 25 July 2024. https://doi.org/10.1088/1751-8121/ad5bc7. Preprint version. arXiv:2310.09811.**2023.***Wolstenholme primes and group determinants of cyclic groups*with**Naoya Yamaguchi and Yuka Yamaguchi**. Preprint**2023**. arXiv:2311.00010**2023.***The heat kernel of the asymmetric quantum Rabi model*. J. Phys. A: Math. Theor.**56**425302, 2023. doi:10.1088/1751-8121/acfbc8. Preprint version arxiv:2012.13595.**2023**.*Covering models of the asymmetric quantum Rabi model: η-shifted non-commutative harmonic oscillators*with**Masato Wakayama**. Comm. Math. Phys. 2023. Published Online 25 August 2023. doi:10.1007/s00220-023-04825-3. SharedIt link (read-only version here)**2023.***Zeta limits for the spectrum of quantum Rabi models*with**Masato Wakayama**. Preprint 2023. arXiv:2304.08943.**2022**.*Heat kernel for the quantum Rabi model*with**Masato Wakayama**. Adv. Theor. Math. Phys.**26**(5), 2022. doi:https:10.4310/ATMP.2022.v26.n5.a8**2022**.*Degeneracy and symmetry hidden 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.**2021.***Heat kernel for the quantum Rabi model II: propagators and spectral determinants*with**Masato Wakayama**. Phys. A: Math. Theor.**54**115202, 2021. doi:10.1088/1751-8121/abdca7.**2020.***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.**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

## Research projects

- Crypto-Math CREST. I am a member in the group lead by Masato Wakayama.
- Grant-in-Aid for Early-Career Scientists (JSPS KAKENHI). Project:
*Number theory and geometry behind quantum interaction models*. Project Number 24K16941. 2024-2026. - AIP Challenge Program 2023 (JST)
- AIP Challenge Program 2022 (JST)

## Activities

- Member of the Mathematical Society of Japan (since 2017).
- Member of Sociedad Matemática Mexicana (since 2019).
- Active reviewer for Mathematical Reviews (MathSciNet) of the AMS (My Profile) and zbMATH Open (My Profile).