Spin relaxation in radical pairs from the stochastic Schr\"odinger equation

TL;DR

This paper demonstrates that the stochastic Schrödinger equation (SSE) effectively simulates quantum spin dynamics in radical pairs, including relaxation effects, and offers advantages over existing methods in efficiency and applicability.

Contribution

It introduces the use of SSE for simulating radical pair spin dynamics with relaxation, outperforming previous stochastic methods and validating approximate theories.

Findings

SSE provides a more efficient simulation than Lindblad approaches.

The method accurately models spin relaxation in radical pairs.

Trace sampling with SU(N) coherent states enhances computational efficiency.

Abstract

We show that the stochastic Schr\"odinger equation (SSE) provides an ideal way to simulate the quantum mechanical spin dynamics of radical pairs. Electron spin relaxation effects arising from fluctuations in the spin Hamiltonian are straightforward to include in this approach, and their treatment can be combined with a highly efficient stochastic evaluation of the trace over nuclear spin states that is required to compute experimental observables. These features are illustrated in example applications to a flavin-tryptophan radical pair of interest in avian magnetoreception, and to a problem involving spin-selective radical pair recombination along a molecular wire. In the first of these examples, the SSE is shown to be both more efficient and more widely applicable than a recent stochastic implementation of the Lindblad equation, which only provides a valid treatment of relaxation in the extreme-narrowing limit. In the second, the exact SSE results are used to assess the accuracy of a recently-proposed combination of Nakajima-Zwanzig theory for the spin relaxation and Schulten-Wolynes theory for the spin dynamics, which is applicable to radical pairs with many more nuclear spins. An appendix analyses the efficiency of trace sampling in some detail, highlighting the particular advantages of sampling with SU(N) coherent states.