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Floquet theory of radical pairs in radiofrequency magnetic fields
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Strictly speaking, this is not broadband noise, but rather a broadband “frequency comb.” A RF signal with two or more incommensurate base frequencies would provide a better description of broadband noise. It is possible to generalise the present theory to deal with such a signal, by adopting a multimode version of Floquet theory of the sort described in Refs. 24 and 30. However, this generalisation breaks down whenever nω1 + mω2 ≃ 0, which can certainly happen when there are many Fourier components in each mode. For our target application, we feel that it is more important to include many Fourier components within a given RF band than to have a faithful description of true “noise,” and for this a frequency comb is ideal.
W. Lersch and M. E. Michel-Beyerle, in Advanced EPR. Applications in Biology and Biochemistry, edited by A. J. Hoff (Elsevier, Amsterdam, 1989), p. 685.
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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.
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