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

• Main Authors: Paterek, Tomasz, Kaszlikowski, D., Chia, A., Tan, K. C., Pawela, Ł., Kurzyński, P.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2018
• Subjects: Coherent Transition; Reaction Kinetics; DRNTU::Science::Physics
• Online Access: https://hdl.handle.net/10356/80445; http://hdl.handle.net/10220/46541
• Institution: Nanyang Technological University

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.