Cid Reyes Bustos

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.

• 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 November 2024.

• 2024/11 The paper Wolstenholme primes and group determinants of cyclic groups was published in Proc. Japan Acad. Ser. A Math. Sci.
• 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.

Visit the publications page for the complete list of publications.

• 2024. Wolstenholme primes and group determinants of cyclic groups with Naoya Yamaguchi and Yuka Yamaguchi. Proc. Japan Acad. Ser. A Math. Sci. 100(9): 51-55 (November 2024). doi:10.3792/pjaa.100.011. Preprint version arXiv:2311.00010.
• 2024. Zeta limits for the spectrum of quantum Rabi models with Masato Wakayama. J. Math. Phys. 1 September 2024; 65 (9): 093503. doi:10.1063/5.0217399.
• 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. 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)
• 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

• 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)

• 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).