An open quantum system approach to the radical pair mechanism

Betony Adams,Ilya Sinayskiy,Francesco Petruccione

doi:10.1038/s41598-018-34007-4

Abstract

The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.

Highlights

For different values of j the scalar product of the state vectors is zero and the space of the total system can be decomposed as the sum of the subspaces[23,25], N ⊗ i2 i=1 s=ym ⊗2 j=0,1 2 ν(N, j) 2j+1, (2)where ν(N, j) is the degeneracy corresponding to a specific value of j and is given by ν(N, j) = N − − N −j ( ) ( ) =
Any further dynamics relating to production of singlet or triplet specific chemicals would still need to be added to the master equation
The open quantum systems approach to the radical pair mechanism presented in this paper demonstrated a novel theoretical approach as well as a novel numerical result

Summary

Results

What is interesting is that the strength of the coupling constant does not dominantly influence the coherence lifetime of the radical pair Where both nuclei interact with comparable magnitude (both of the order of 107 for Graph (a) and both of the order of 104 for Graph (b)) the dissipation happens more slowly whereas if the two nuclei have markedly different coupling magnitudes (Graph (c)) the dissipation happens more quickly. This is because in the latter configuration a greater proportion of the transition frequencies give rise to quicker transition rates. The model further demonstrates that it is sufficient to have one nucleus with larger coupling constant for the oscillation to be ensured (Graph (c) inset)

Introduction

Methods

Discussion