Optimal control of the external electromagnetic field input for the maximization of the quantum triplet-singlet yield of the radical pairs in biochemical reactions modeled by Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms are analyzed. Fréchet differentiability and Pontryagin Maximum Principle in Hilbert space is proved and the bang-bang structure of the optimal control is established. A closed optimality system of nonlinear differential equations for the identification of the bang-bang optimal control is revealed. Numerical methods for the identification of the bang-bang optimal control based on the Pontryagin maximum principle are developed. Numerical simulations are pursued, and the convergence and stability of the numerical methods are demonstrated. The results contribute towards understanding the structure-function relationship of the putative magnetoreceptor to manipulate and enhance quantum coherences at room temperature and leveraging biofidelic function to inspire novel quantum devices.

中文翻译：

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量子生物学中自由基对相干自旋动力学的 Bang-bang 最优控制


分析了外部电磁场输入的优化控制，以最大化生化反应中自由基对的量子三重态-单重态产率，该系统由薛定谔系统建模，自旋哈密顿量由塞曼相互作用和超精细耦合相互作用项的总和给出。证明了Hilbert空间中的Fréchet可微性和Pontryagin极大值原理，建立了最优控制的bang-bang结构。揭示了用于识别 Bang-Bang 最优控制的非线性微分方程的闭合最优系统。开发了基于庞特里亚金极大值原理的 bang-bang 最优控制辨识的数值方法。进行了数值模拟，并证明了数值方法的收敛性和稳定性。这些结果有助于理解假定的磁感受器的结构-功能关系，以在室温下操纵和增强量子相干性，并利用生物逼真功能来激发新型量子器件。