Pontryagin Maximum Principle in optimal control of coherent spin dynamics of radical pairs in Quantum Biology II. Computational Analysis
Mr. Pablo Jimenez, Instituto Balseiro, Universidad Nacional de Cuyo, Phd Student
Dr. Jose Rodriques, OIST, Analysis and Partial Differential Equations Unit(Abdulla Unit),Staff Scientist
Mr. Chenming Zhen, OIST, Phd Student
The advance of physics and technology has allowed researchers to explore and verify quantum phenomena in areas such as chemistry and biology. In particular, the applicability of optimal control theory to solve the problem of identification of magnetic field and/or hyperfine parameters related to free radical pairs has been proven a fruitful source of problems and research that contributes to the development of the new area of quantum biology. Based on rigorous mathematical theoretical analysis, Bang-bang type control of magnetic field and hyperfine parameters is proven to give maximization of singlet-triplet yield. Computational analysis follows the theoretical results to demonstrate how Bang-bang optimal control behaves in different situations. Two algorithms, one following Pontrygin's Maximum Principle and one following Gradient Projection Method, will be presented. The algorithms are adapted in three situations, where only magnetic field, only hyperfine parameter and both parameters will be examined. The results from individual algorithms will be presented to comprehend the theories while the difficulties and limitations of each algorithm will be detailed. The adaptation of using two algorithms together will also be demonstrated and the advantage of such adaptation will be shown through simulations in comparison of individual-algorithm results.