Quantum Klein-Gordon model of Quantum Many-BodyHysteresis in Topological Insulators for Hydrogen Switching inMg-Ni Alloys and CO2 Reduction Catalysis

  • Authors

    • Isamu Ohnishi Faculty of Mathematical Science, Graduate School of Integrated Sciences for Life, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima, Hiroshima-Pref., JAPAN 739-8526
    https://doi.org/10.14419/en094q27
  • Quantum Many-Body Hysteresis, Topological Insulators, Renormalization Group, Nonlinear Klein-Gordon, Hydrogen Storage, Sustainable Catalysis (AMS Classification NO.s: 81V70, 37N20, 81Q60, 82C31, 81P68)

  • Abstract

    This work integrates the Simple Binary Memory (SBM-ODE) model with topological insulator (TI) dynamics and quantum

    many-body hysteresis, extending to quantum Klein-Gordon (KG) frameworks for hydrogen switching in Mg-Ni alloys and CO2

    reduction. We canonically quantize Duffing oscillator chains to derive quantum KG equations, incorporating synchronization

    for efficient absorption/desorption. Using Chiba’s Renormalization Group Method (RGM), we prove SU(2)-symmetry

    breaking preservation via Schur’s lemma, derive scale-dependent flows for N-dependent hysteresis, and evaluate Hartree-

    Fock-Bogoliubov (HFB) self-consistency. Numerical simulations with QuTiP show oscillatory ⟨σz⟩ (amplitude ∼0.1, period

    5) with damping in quantum KG under Mg-Ni lattice, confirming winding number shifts (w: 1 → 0 at μ = ±2t). Model

    Predictive Control (MPC) optimizes multi-electron transfers, yielding 15-25% improvements. This bridges spintronics,

    quantum materials, and sustainable energy, aligning with 2025 trends in topological many-body systems[15][33][1].

  • References

    1. Charlotte Boettcher, Ashvin Vishwanath, Xiaodong Xu, and Matthew Yankowitz. Topological quantum many-body systems.
    2. Aspen Center for Physics, 2025. https://aspenphys.org/event/topological-quantum-many-body-systems/.
    3. Heinz-Peter Breuer and Francesco Petruccione. The theory of open quantum systems. Oxford University Press, 2002.
    4. Weibin Chen, Menghui Bao, Fanqi Meng, Bingbing Ma, Long Feng, and Xuan Zhang. Designer topological-single-atom catalysts
    5. with site-specific selectivity. Nature Communications, 2025.
    6. Hayato Chiba. Renormalization group method for reduction of differential equations. SIAM Journal on Applied Dynamical
    7. Systems, 8(3):1076–1106, 2009.
    8. Hayato Chiba. Simplified renormalization group method for ordinary differential equations. SIAM Journal on Applied Dynamical
    9. Systems, 2009.
    10. Hayato Chiba. High-order renormalization group for nonlinear systems. Journal of Mathematical Physics, 61(6):062701, 2020.
    11. Hayato Chiba. Normal forms of c∞ vector fields based on the renormalization group. Journal of Mathematical Physics, 62(6):062703,
    12. Shuya Dong, Zhilong Song, and Jianfeng Jia. Exploration and design of mg alloys for hydrogen storage with targeted property
    13. improvement using machine learning. International Journal of Hydrogen Energy, 2024.
    14. Shin-Ichiro Ei, Kazuyuki Fujii, and Teiji Kunihiros. Renormalization-group method for reduction of evolution equations. Journal
    15. of Mathematical Physics, 1999.
    16. Ivan Gilardoni, Federico Becca, Antimo Marrazzo, and Nicola Marzari. Real-space many-body marker for correlated topological
    17. insulators. Physical Review B, 2024.
    18. J. Gu, J. Huang, Z. Jin, and T. Wei. Multidimensional engineering of zif-8-based electrocatalysts for co2rr. RSC, 2025.
    19. https://pubs.rsc.org/en/content/articlelanding/2025/cc/d5cc03189c.
    20. Dominik Hahn and Juan Felipe Rodriguez-Nieva. Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices.
    21. Physical Review E, 2021.
    22. Jonah Herzog-Arbeitman, B. Andrei Bernevig, and Zhi-Da Song. Interacting topological quantum chemistry in 2d with many-body
    23. real-space invariants. Nature Communications, 2024.
    24. Xiangting Hu, Xiang Huang, Peiyao Qin, Chao He, and Hu Xu. Redefining catalyst design in topological materials. Physical
    25. Review B, 2024.
    26. Olivier Huber. Optical control over topological chern number in moir’e materials. arXiv, 2025. https://arxiv.org/html/2508.
    27. v1.
    28. Kunihiko Kaneko and Mari Tsubota. Non-equilibrium ϕ4 theory in open systems as a toy model of quantum field theory of the
    29. real scalar field. Annals of Physics, 2018.
    30. Xiangdong Kong, Jiawei Wan, Zhen Zhang, Shibo Xi, Ming Xu, Yonghua Du, Binbin Chang, Xiao Wang, Qing Kang, Chen Chen,
    31. Bingcai Pan, Shuai Yuan, Wei Chen, Jun Li, Chen-Gang Wang, Bin Wang, Yong Xu, and Lei Jiang. Experimental demonstration
    32. of topological catalysis for co2 electrochemical reduction. Journal of the American Chemical Society, 2024.
    33. Nitesh Kumar, Satya N. Guin, Kaustuv Manna, and Chandra Sekhar M. Topological quantum materials from the viewpoint of
    34. chemistry. ACS Chem. Rev., 2020. https://pubs.acs.org/doi/10.1021/acs.chemrev.0c00732.
    35. Yoshiki Kuramoto. Chemical oscillations, waves, and turbulence. Springer, 1984.
    36. Yang Liu, Chuanliang Zhao, and Haotian Wang. Experimental demonstration of topological catalysis for co2 electrochemical
    37. reduction. JACS, 2024. https://pubs.acs.org/doi/abs/10.1021/jacs.3c11088.
    38. Xinliang Lyu. Three-dimensional real space renormalization group with well-defined fixed-point tensor. arXiv, 2025. https:
    39. //arxiv.org/html/2412.13758v2.
    40. Jingyi Ma, Yujie Bai, Zhiyuan Zhang, Xiaohui Deng, Hongliang Dong, and Zhigang Zou. Co2 reduction reactivity on the sic
    41. monolayer with doped 585 extended line defects: A computational study. Energy & Fuels, 2024.
    42. Isamu Ohnishi. Nonlinear klein-gordon dynamics and control via chiba-rg in mg-ni alloy hydrogen storage. Preprint (in submitting),
    43. Isamu Ohnishi. Rigorous analysis of langevin noise effects on hysteresis in simplified binary memory models: Classical and quantum
    44. dynamics for co2 reduction catalysis. Preprint (in submittion), 2025. submit arXiv 6829258.
    45. Isamu Ohnishi. Rigorous renormalization group analysis of quantum many-body hysteresis in topological insulators: Applications
    46. to hydrogen switching and co2 reduction catalysis. Preprint (in submittion), 2025. https://papers.ssrn.com/sol3/papers.cfm?
    47. abstract_id=5490827.
    48. Isamu Ohnishi. Topological insulator dynamics with hydrogen on-off switching: Capacity improvement by mpc method via chiba
    49. rigorous renormalization group in view of control theory. American J. Engineering Research, 2025.
    50. P. H. S. Palheta, P. E. G. Assis, T. M. Nogueira, J. M. S. Ferreira, and A. S. L. Malheiro. The evolution of spectral data for
    51. nonlinear klein-gordon models. arXiv preprint arXiv:2408.10101, 2024.
    52. Junqi Qiu, Mingxia Gao, Yongquan Qing, and Hongge Yan. Tailoring hydrogen diffusion pathways in mg-ni alloys through gd
    53. substitution and its impact on hydrogen storage properties. Chemical Engineering Journal, 2024.
    54. Saurabh Kumar Singh and Sumantra Bhattacharya. Unconventional and emerging approaches to co2 reduction. Sustainability,
    55. Bo Song, Wentao Song, Yuhang Liang, Yong Liu, Bowen Li, He Li, Liang Zhang, Yanhang Ma, Ruquan Ye, Ben Zhong
    56. Tang, Dan Zhao, and Bin Liu. Yi Zhou. Direct synthesis of topology-controlled bodipy and co2-based zr-mofs. PubMed, 2025.
    57. https://pubmed.ncbi.nlm.nih.gov/39742452/.
    58. P. Stanley, Karina Hemmer, Lea N. Winter, Jonathan A. Steele, Dirk E. De Vos, and Karolien Jans. Topology- and wavelengthgoverned
    59. co2 reduction photocatalysis in molecular catalyst-metal-organic framework hybrids. Chemical Communications, 2022.
    60. Duy Van Tran and Duc Ba Nguyen. Tailoring hydrogen storage performance of mg-mg2ni alloys by fine-tuning the phase
    61. compositions and morphologies. Nanoscale, 2025.
    62. Bent Weber, Michael S. Fuhrer, Xian-Lei Sheng, Shengyuan A. Yang, Ronny Thomale, Saquib Shamim, Laurens W. Molenkamp,
    63. David Cobden, Dmytro Pesin, and Harold J. W. Zandvliet. 2024 roadmap on 2d topological insulators. IOPscience, 2024.
    64. https://iopscience.iop.org/article/10.1088/2515-7639/ad2083.
    65. Chao Zhang, Huichao Wang, Rui Chen, Zaichen Xiang, Yongqing Cai, Kai Yan, Kangwang Wang, Huixia Luo, Longfu Li, and
    66. Peifeng Yu. Revealing the nontrivial topological surface states of catalysts for effective photochemical co2 conversion. Applied
    67. Catalysis B: Environmental, 2024.

  • Downloads

  • How to Cite

    Ohnishi, I. (2026). Quantum Klein-Gordon model of Quantum Many-BodyHysteresis in Topological Insulators for Hydrogen Switching inMg-Ni Alloys and CO2 Reduction Catalysis. International Journal of Advanced Mathematical Sciences, 12(1), 39-47. https://doi.org/10.14419/en094q27