math [at] cidrb . me

Cid Reyes Bustos

Mathematician

About me

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.

Research interests

  • 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.

Upcoming talks

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.

News

  • 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..

Main Publications and preprints

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

Activities

  • 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).

Links