Cid Reyes Bustos

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• 3. Wolstenholme primes and group determinants of cyclic groups with Naoya Yamaguchi and Yuka Yamaguchi. Preprint 2023. arXiv:2311.00010
• 2. Spacing distribution for quantum Rabi models with Daniel Braak, Linh Thi Hoai Nguyen and Masato Wakayama. Preprint 2023. arXiv:2310.09811.
• 1. Zeta limits for the spectrum of quantum Rabi models with Masato Wakayama. Preprint 2023. arXiv:2304.08943.

• 11. Towards hash functions based on group-subgroup pair graphs. Book chapter. To Appear, 2024.
• 10. 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.
• 9. 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). Preprint 2022. arXiv:2209.14665.
• 8. Heat kernel for the quantum Rabi model with Masato Wakayama. Adv. Theor. Math. Phys. 26 (5), 1347-1447, 2022. doi:https:10.4310/ATMP.2022.v26.n5.a8. Preprint: arxiv:1906.09597.
• 7. Degeneracy and hidden symmetry 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.
• 6. 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
• 5. Heat kernel for the quantum Rabi model II: propagators and spectral determinants with Masato Wakayama. J. Phys. A: Math. Theor. 54 115202, 2021. doi:10.1088/1751-8121/abdca7. Preprint 2020. arXiv:2008.05354
• 4. 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. 2020 doi:10.1007/978-981-15-5191-8_13
• 3. 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. doi:10.1093/imrn/rnaa034. Preprint version arxiv:1712.04152.
• 2. 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
• 1. 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
  • An accepted manuscript version is available here. The Mathematica source code for the figure files is available here.

• 4. The heat kernel of the quantum Rabi model and related models. RIMS Kôkyûroku 2200 (2021). Spectral and Scattering Theory and Related Topics. http://hdl.handle.net/2433/266214
• 3. Degeneracy structure of the spectrum of the asymmetric quantum Rabi model. RIMS Kôkyûroku 2123 (2019). Mathematical aspects of quantum fields and related topics. http://hdl.handle.net/2433/252192
  • This is a summary of Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model.
• 2. Orthogonal polynomials related to the asymmetric quantum Rabi model. Proceedings of the Symposium on Representation Theory 2018 年度表現論シンポジウム講演集. doi.org/10.34508/repsympo.2018.0_121.
• 1. Group-subgroup pair graphs. RIMS Kôkyûroku 1925 (2014). New Developments of Representation Theory and Harmonic Analysis. Research Institute for Mathematical Science. Kyoto University. http://hdl.handle.net/2433/223486
  • Please note that the contents of this research report are superseded by Cayley-type graphs for group-subgroup pairs.

• 1. A simple continued fraction expansion for \(e^n\). Preprint 2019. arxiv:1909.13597

• 2018. Study on the spectrum of the asymmetric quantum Rabi model. Doctoral dissertation. Kyushu University. Download from here.
  • This is the basis for the article Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model. The historical background and introduction to the study of the spectrum of the quantum Rabi model Hamiltonian may be useful for some people.
• 2015. Cayley-type graphs for group-subgroup pairs. Master thesis. Kyushu University. Download pdf.
  • The basis for the article Cayley-type graphs for group-subgroup pairs.
• 2010. Braid-group cryptrography (in Spanish). Bachelor thesis. Download here.
  • An overview of several cryptosystems based on braid groups and their cryptanalysis. The design of a python implementation is also included.