Site Number Dependence of Hysteresis in Binary Memory Models via Renormalization Group Approach Application to CO2 Reduction Reaction
DOI:
https://doi.org/10.14419/xz60jv72Published
01-02-2026Keywords:
Binary Memory Model, Hysteresis, Renormalization Group, CO2 Reduction Catalysis, Mean-Field Approximation (AMS Classification NO.s: 34C23, 37C75, 37L10, 82C26, 35Q55)Abstract
This study extends the Binary Digit Memory (BDM) model and explores its application to CO_2 reduction catalysis. Originally developed to model memory induction through covalent modifications, the BDM model is a mathematical framework that describes switching dynamics in systems with multiple sites. We adapt this model for catalytic processes by coupling it with the Schrödinger equation to account for multi-electron dynamics on catalyst surfaces. The research is structured into three main chapters.
Chapter 2: We perform a formal analysis of the BDM-ODE system using the mean-field approximation. This approach simplifies the high-dimensional system and reveals critical phenomena such as hysteresis and bifurcations, which are essential for understanding catalytic behavior.
Chapter 3: We refine these findings using renormalization group (RG) theory, which rigorously justifies the mean-field approximation and uncovers the scaling universality of the system's critical behavior as the number of sites, N , increases. This universality ensures consistency in predictions across different scales.
Chapter 4: We apply this framework to CO₂ reduction. We introduce a coupled system where the Schrödinger equation governs electron dynamics on the catalyst surface, while the BDM-ODE system manages the switching dynamics. Using the Hartree approximation and RG-validated mean-field methods, we simulate the CO₂ reduction process and optimize catalytic performance. Simulations demonstrate significant improvements in yield and efficiency.
This interdisciplinary approach integrates nonlinear dynamics and quantum mechanics, offering new insights into CO₂ reduction catalysis. By leveraging the strengths of the BDM model and combining it with quantum mechanical principles, we establish a robust theoretical foundation for enhancing catalytic processes, with potential implications for sustainable energy solutions.
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