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 September 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 for the periods 22-23 and 23-24.

Conference

Title TBA. Zeta function in Okinawa 2023. October 26-28, 2023.

Conference

"Limits of the spectral zeta function of the quantum Rabi model". Number Theory in Fukuoka. November 9-10, 2023.

• 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.
• 2023/06 I was awarded a the "AIP Challenge Program 2023" grant of AIP Network Laboratories of JST.
• 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..

Visit the publications page for the complete list of publications.

• 2023. The heat kernel of the asymmetric quantum Rabi model. J. Phys. A: Math. Theor. 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. 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:10.1007/978-981-15-5191-8₁₃
• 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.
• 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) and zbMATH Open (My Profile).