Cid Reyes Bustos

I am currently a Research Associate in the NTT Institute for Fundamental Mathematics at the NTT Corporation.

My CV can be downloaded here. Last updated on April 2023.

• Representation theory and orthogonal polynomials.
• Number theory, zeta functions and continued fractions.
• Graph theory, generalizations of Cayley graphs and harmonic analysis of graphs.
• Spectral analysis of quantum Rabi model and non-commutative harmonic oscillator.

I am a member of the Crypto-Math CREST project in the group lead by Masato Wakayama. I was awarded the "AIP Challenge Program" grant of JST for support of independent research in the period 2022-2023.

• 2023/04 The preprint Zeta limits for the spectrum of quantum Rabi models was uploaded to arXiv.
• 2023/03 The paper Heat kernel for the quantum Rabi model was published in Advances in Theorerical and Mathematical Physics, 2022.
• 2023/03 I joined as an organizer for a conference on expander graphs to be held in Kyushu University (see Kyushu IMI site).
• 2023/01 I am an organizer for a mini-symposium in ICIAM 2023. More information here.
• 2022/10 The paper Degeneracy and hidden symmetry for the asymmetric quantum Rabi model with integral bias was published in Communications in Number Theory and Physics, 2022.
• 2022/07 I was awarded a the "AIP Challenge Program 2022" grant of AIP Network Laboratories of JST. Announcement in this link.

Visit the publications page for the complete list of publications.

• 2023. Zeta limits for the spectrum of quantum Rabi models with Masato Wakayama. Preprint 2023. arXiv:2304.08943.
• 2022. Covering models of the asymmetric quantum Rabi model: η-shifted non-commutative harmonic oscillators with Masato Wakayama. Preprint 2022. arXiv:2209.14665.
• 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 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. Preprint 2021 arxiv:2101.04305
• 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. 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
• 2020. The heat kernel of the asymmetric quantum Rabi model. Preprint 2020. arxiv:2012.13595
• 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.
• 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

• Member of the Mathematical Society of Japan (since 2017).
• Member of Sociedad Matemática Mexicana (since 2019).
• I write reviews for Mathematical Reviews (MathSciNet) of the American Mathematical Society (My Profile).