Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2005.04417 · New Journal of Physics

Monte-Carlo wavefunction approach for the spin dynamics of recombining radicals

Robert H. Keens, Daniel R. Kattnig

Published Jul 20, 2020• 9 citations
arXivHTMLPDF

Abstract

Abstract We adapt the Monte-Carlo wavefunction (MCWF) approach to treat the open-system spin dynamics of radical pairs subject to spin-selective recombination reactions. For these systems, non-Lindbladian master equations are widely employed, which account for recombination via the non trace-preserving Haberkorn superoperator in combination with reaction-dependent exchange and singlet–triplet dephasing terms. We show that this type of master equation can be accommodated in the MCWF approach, by introducing a second type of quantum jump that accounts for the reaction simply by suitably terminating the propagation. In this way, we are able to evaluate approximate solutions to the time-dependent radical pair survival probability for systems that have been considered untreatable with the master equation approach until now. We explicate the suggested approach with calculations for radical pair reactions that have been suggested to be relevant for the quantum compass of birds and related phenomena.

DOI
10.1088/1367-2630/aba76d

Related papers

Consistent Treatment of Spin-Selective Recombination of a Radical Pair Confirms the Haberkorn Approach

Konstantin L. Ivanov, Marina V. Petrova, Nikita N. Lukzen +1 more

In the present work, we have shown that consistent derivation of the kinetic equations describing the electron spin-selective recombination of radical pairs confirms the conventional Haberkorn approach. The derivation has been based on considering the interaction of the reactive system (radical pair and product state) with the thermal bath. The consistency of this approach has also been substantiated by numerical simulations performed for the purely quantum mechanical model of the recombining radical pair. Finally, we have shown that the quantum Zeno effect on radical pair recombination is not an exclusive feature of the approach recently proposed by Kominis, as it should be present at any rate of the singlet-triplet dephasing in the radical pair, which always accompanies the recombination process.

The Journal of Physical Chemistry A•Aug 12, 2010•68 citations

Multiple re-encounter approach to radical pair reactions and the role of nonlinear master equations

Jens Clausen, Gian Giacomo Guerreschi, Markus Tiersch +1 more

We formulate a multiple-encounter model of the radical pair mechanism that is based on a random coupling of the radical pair to a minimal model environment. These occasional pulse-like couplings correspond to the radical encounters and give rise to both dephasing and recombination. While this is in agreement with the original model of Haberkorn and its extensions that assume additional dephasing, we show how a nonlinear master equation may be constructed to describe the conditional evolution of the radical pairs prior to the detection of their recombination. We propose a nonlinear master equation for the evolution of an ensemble of independently evolving radical pairs whose nonlinearity depends on the record of the fluorescence signal. We also reformulate Haberkorn's original argument on the physicality of reaction operators using the terminology of quantum optics/open quantum systems. Our model allows one to describe multiple encounters within the exponential model and connects this with the master equation approach. We include hitherto neglected effects of the encounters, such as a separate dephasing in the triplet subspace, and predict potential new effects, such as Grover reflections of radical spins, that may be observed if the strength and time of the encounters can be experimentally controlled.

arXiv:1310.6194•The Journal of Chemical Physics•Aug 5, 2014•10 citations

Retrodictive derivation of the radical-ion-pair master equation and Monte Carlo simulation with single-molecule quantum trajectories

Michail Kritsotakis, Iannis K. Kominis

Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011)]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.

arXiv:1407.7757•Physical Review E•Oct 21, 2014•11 citations

Describing Spin-Selective Reactions of Radical Pairs Using Quantum Jump Approaches

Alpha A. Lee

Recently, spin-selective radical pair reactions have been studied using concepts from quantum measurement theory. In this Article, we show that the approach taken by Kominis (Physical Review E, 83, 2011, 056118) leads to erroneous results due to a problematic treatment of quantum jumps. Correct consideration of quantum jumps leads to either the traditional master equation or the Jones-Hore master equation.

arXiv:1110.2298•Oct 11, 2011•0 citations

F-cluster: Reaction-induced spin correlation in multi-radical systems

DR Kattnig (21871391)

We provide a theoretical analysis of spin-selective recombination processes in clusters of n ≥ 3 radicals. Specifically, we discuss how spin correlation can ensue from random encounters of n radicals, i.e., "F-clusters" as a generalization of radical F-pairs, acting as precursors of spin-driven magnetic field effects. Survival probabilities and the spin correlation of the surviving radical population, as well as transients, are evaluated by expanding the spin density operator in an operator basis that is closed under application of the Haberkorn recombination operator and singlet-triplet dephasing. For the primary spin cluster, the steady-state density operator is found to be independent of the details of the recombination network, provided that it is irreducible; pairs of surviving radicals are triplet-polarized independent of whether they are actually reacting with each other. The steady state is independent of the singlet-triplet dephasing, but the kinetics and the population of sister clusters of smaller size can depend on the degree of dephasing. We also analyze reaction-induced singlet-triplet interconversion in radical pairs due to radical scavenging by initially uncorrelated radicals ("chemical Zeno effect"). We generalize previous treatments for radical triads by discussing the effect of spin-selective recombination in the original pair and extending the analysis to four radicals, i.e., radical pairs interacting with two radical scavengers.

•Aug 1, 2025•0 citations

New developments in open quantum system dynamics

Lachlan P. Lindoy

The dynamics of many chemical systems can be influenced significantly by interactions with their environment (bath). An exact treatment of this is often infeasible due to the exponential scaling of Hilbert space with the number of degrees of freedom. In this thesis, dynamical methods, which overcome this difficulty, are considered for spin systems coupled to spin baths as well as systems coupled to harmonic oscillator baths. The thesis begins by considering recombination reactions of radical pairs, in which two electron spins interact with baths of nuclear spins. Motivated by inaccuracies observed in semiclassical treatments of the dynamics of a series of cryptochrome-based radical pairs, a new approach capable of treating the quantum dynamics of spin systems coupled to large baths of spins is presented. This method is validated for a series of central spin models, and is found to correctly describe the quantum dynamics of spin systems containing up to 1000 spins. Following this, the validity of the conventional treatment of radical pair recombination reactions is explored by considering the coupled electronic, nuclear and spin dynamics of a model radical ion pair. The dynamics of this model is treated using the hierarchical equations of motion (HEOM) formalism, and the results obtained are used to validate a recently proposed series of master equations. The HEOM formalism exactly captures the quantum dynamics of systems that are coupled to harmonic baths. However, due to the scaling of its computational cost with the strength of the coupling, it often becomes impractical. To overcome this difficulty, an efficient tree tensor network-based approach is presented and valided by treating a series of simple models. Following this, it is applied to the calculation of electron transfer rates for a series of models spanning a wide range of physical regimes in order to validate a recently proposed interpolation formula for the calculation of electron transfer rates.

•Jan 1, 2019•1 citation
Abstract We adapt the Monte-Carlo wavefunction (MCWF) approach to treat the open-system spin dynamics of radical pairs subject to spin-selective recombination reactions. For these systems, non-Lindbladian master equations are widely employed, which account for recombination via the non trace-preserving Haberkorn superoperator in combination with reaction-dependent exchange and singlet–triplet dephasing terms. We show that this type of master equation can be accommodated in the MCWF approach, by introducing a second type of quantum jump that accounts for the reaction simply by suitably terminating the propagation. In this way, we are able to evaluate approximate solutions to the time-dependent radical pair survival probability for systems that have been considered untreatable with the master equation approach until now. We explicate the suggested approach with calculations for radical pair reactions that have been suggested to be relevant for the quantum compass of birds and related phenomena.
In the present work, we have shown that consistent derivation of the kinetic equations describing the electron spin-selective recombination of radical pairs confirms the conventional Haberkorn approach. The derivation has been based on considering the interaction of the reactive system (radical pair and product state) with the thermal bath. The consistency of this approach has also been substantiated by numerical simulations performed for the purely quantum mechanical model of the recombining radical pair. Finally, we have shown that the quantum Zeno effect on radical pair recombination is not an exclusive feature of the approach recently proposed by Kominis, as it should be present at any rate of the singlet-triplet dephasing in the radical pair, which always accompanies the recombination process.
We formulate a multiple-encounter model of the radical pair mechanism that is based on a random coupling of the radical pair to a minimal model environment. These occasional pulse-like couplings correspond to the radical encounters and give rise to both dephasing and recombination. While this is in agreement with the original model of Haberkorn and its extensions that assume additional dephasing, we show how a nonlinear master equation may be constructed to describe the conditional evolution of the radical pairs prior to the detection of their recombination. We propose a nonlinear master equation for the evolution of an ensemble of independently evolving radical pairs whose nonlinearity depends on the record of the fluorescence signal. We also reformulate Haberkorn's original argument on the physicality of reaction operators using the terminology of quantum optics/open quantum systems. Our model allows one to describe multiple encounters within the exponential model and connects this with the master equation approach. We include hitherto neglected effects of the encounters, such as a separate dephasing in the triplet subspace, and predict potential new effects, such as Grover reflections of radical spins, that may be observed if the strength and time of the encounters can be experimentally controlled.
Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011)]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.
We provide a theoretical analysis of spin-selective recombination processes in clusters of n ≥ 3 radicals. Specifically, we discuss how spin correlation can ensue from random encounters of n radicals, i.e., "F-clusters" as a generalization of radical F-pairs, acting as precursors of spin-driven magnetic field effects. Survival probabilities and the spin correlation of the surviving radical population, as well as transients, are evaluated by expanding the spin density operator in an operator basis that is closed under application of the Haberkorn recombination operator and singlet-triplet dephasing. For the primary spin cluster, the steady-state density operator is found to be independent of the details of the recombination network, provided that it is irreducible; pairs of surviving radicals are triplet-polarized independent of whether they are actually reacting with each other. The steady state is independent of the singlet-triplet dephasing, but the kinetics and the population of sister clusters of smaller size can depend on the degree of dephasing. We also analyze reaction-induced singlet-triplet interconversion in radical pairs due to radical scavenging by initially uncorrelated radicals ("chemical Zeno effect"). We generalize previous treatments for radical triads by discussing the effect of spin-selective recombination in the original pair and extending the analysis to four radicals, i.e., radical pairs interacting with two radical scavengers.
The dynamics of many chemical systems can be influenced significantly by interactions with their environment (bath). An exact treatment of this is often infeasible due to the exponential scaling of Hilbert space with the number of degrees of freedom. In this thesis, dynamical methods, which overcome this difficulty, are considered for spin systems coupled to spin baths as well as systems coupled to harmonic oscillator baths. The thesis begins by considering recombination reactions of radical pairs, in which two electron spins interact with baths of nuclear spins. Motivated by inaccuracies observed in semiclassical treatments of the dynamics of a series of cryptochrome-based radical pairs, a new approach capable of treating the quantum dynamics of spin systems coupled to large baths of spins is presented. This method is validated for a series of central spin models, and is found to correctly describe the quantum dynamics of spin systems containing up to 1000 spins. Following this, the validity of the conventional treatment of radical pair recombination reactions is explored by considering the coupled electronic, nuclear and spin dynamics of a model radical ion pair. The dynamics of this model is treated using the hierarchical equations of motion (HEOM) formalism, and the results obtained are used to validate a recently proposed series of master equations. The HEOM formalism exactly captures the quantum dynamics of systems that are coupled to harmonic baths. However, due to the scaling of its computational cost with the strength of the coupling, it often becomes impractical. To overcome this difficulty, an efficient tree tensor network-based approach is presented and valided by treating a series of simple models. Following this, it is applied to the calculation of electron transfer rates for a series of models spanning a wide range of physical regimes in order to validate a recently proposed interpolation formula for the calculation of electron transfer rates.