Floquet theory of radical pairs in radiofrequency magnetic fields

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. Published by AIP Publishing. [http://dx

Disruption of Magnetic Compass Orientation in Migratory Birds by Radiofrequency Electromagnetic Fields

“…2 as an additional, time-dependent Zeeman term. This severely complicates simulation of even simple spin systems, but an approximate Floquet method significantly simplifies the calculation (21). The basis of the algorithm is to consider degeneracies between states in the extended ''Floquet space'', whose energies are shifted by integer multiples of the base frequency in the applied field.…”

“…These degeneracies therefore correspond to the external fields being resonant with an energy gap in the spin system. Assuming these resonances account for the important physics in the problem, we can exploit the weakness of the time-dependent fields and slow radical-pair recombination to derive a viable perturbation method based on diagonalization of a single Hilbert-space-sized matrix (21). Although single-frequency fields are straightforward to model, the details of the Floquet method mean that we must mimic the broadband noise using a ''comb'' of frequency components, spaced (in this case) by 1 kHz (21).…”

“…Theoretical studies complementary to the behavioral experiments are currently limited, being severely hampered by the computational challenges. Using a recently developed approach (21), we examine the behavior of radical pairs in silico subject to an approximation to the conditions of the behavioral experiments. On the basis of these simulations, we discuss how it might be possible to discriminate experimentally between different radical pairs and to determine more convincingly than hitherto whether the sensory mechanism is indeed based on radical pairs.…”

Molecular dynamics simulations disclose early stages of the photo-activation of cryptochrome 4

“…Interestingly, radical pair magnetoreception is considered a truly quantum process in a biological environment [31]. The underlying coherent spin dynamics are a topic of much current research [29,[32][33][34][35][36][37][38][39]. Here, we focus on the processes that follow up on this initial stage.…”

Radical-pair-based magnetoreception in birds: radio-frequency experiments and the role of cryptochrome

“…It is not even clear if the local Larmor-RF condition was always exactly matched in each experimental trial so as to produce the maximum resonance effect. If a 25 nT single-frequency magnetic field is to have an effect on the spin dynamics in a radical pair, it has to act upon the spin-correlated pair for longer than 200 μs (Hiscock et al 2016), which implies that its resonance frequency is sharper than 5 kHz, ca. 0.5% in terms of the absolute frequency (5/1315).…”