Floquet theory of radical pairs in radiofrequency magnetic fields

TL;DR

This paper introduces a Floquet theory-based method to efficiently calculate radical pair reaction yields under weak radiofrequency magnetic fields, enabling studies of biological magnetoreception with more complex models.

Contribution

A novel Floquet theory approach that approximates radical pair yields in time-dependent magnetic fields, reducing computational complexity and allowing for larger, more realistic systems.

Findings

Method accurately matches exact quantum results for simple models.

Significantly reduces computational effort compared to traditional methods.

Applicable to complex radical pairs with many nuclear spins.

Abstract

We present a new method for calculating the product yield of a radical pair recombination reaction in the presence of a weak time-dependent magnetic field. This method successfully circumvents the computational difficulties presented by a direct solution of the Liouville-von Neumann equation for a long-lived radical pair containing many hyperfine-coupled nuclear spins. Using a modified formulation of Floquet theory, treating the time-dependent magnetic field as a perturbation, and exploiting the slow radical pair recombination, we show that one can obtain a good approximation to the product yield by considering only nearly-degenerate sub-spaces of the Floquet space. Within a significant parameter range, the resulting method is found to give product yields in good agreement with exact quantum mechanical results for a variety of simple model radical pairs. Moreover it is considerably more efficient than the exact calculation, and it can be applied to radical pairs containing significantly more nuclear spins. This promises to open the door to realistic theoretical investigations of the effect of radiofrequency electromagnetic radiation on the photochemically induced radical pair recombination reactions in the avian retina which are believed to be responsible for the magnetic compass sense of migratory birds.