Coherent chemical kinetics as quantum walks. II. Radical-pair reactions in Arabidopsis thaliana

Numerical tests of magnetoreception models assisted with behavioral experiments on American cockroaches

Many animals display sensitivity to external magnetic field, but it is only in the simplest organisms that the sensing mechanism is understood. Here we report on behavioural experiments where American cockroaches (Periplaneta americana) were subjected to periodically rotated external magnetic fields with a period of 10 min. The insects show increased activity when placed in a periodically rotated Earth-strength field, whereas this effect is diminished in a twelve times stronger periodically rotated field. We analyse established models of magnetoreception, the magnetite model and the radical pair model, in light of this adaptation result. A broad class of magnetite models, based on single-domain particles found in insects and assumption that better alignment of magnetic grains towards the external field yields better sensing and higher insect activity, is shown to be excluded by the measured data. The radical-pair model explains the data if we assume that contrast in the chemical yield on the order of one in a thousand is perceivable by the animal, and that there also exists a threshold value for detection, attained in an Earth-strength field but not in the stronger field.

Coherent chemical kinetics as quantum walks. I. Reaction operators for radical pairs

Classical chemical kinetics uses rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, in other words, a reaction that contains only incoherent transitions. A prominent example of a reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator that determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts the same recombination dephasing rate as the conventional Haberkorn model, which is consistent with recent experiments [K. Maeda et al., J. Chem. Phys. 139, 234309 (2013)], in contrast to previous work by Jones and Hore [J. A. Jones and P. J. Hore, Chem. Phys. Lett. 488, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalized density operator incorporating both the radical pair and reaction products or a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalized and refers only to radical-pair states. Generalizations to include additional dephasing processes and an arbitrary number of sites are also discussed.