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:1110.2298

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

Alpha A. Lee

Published Oct 11, 2011• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1110.2298

Related papers

Entropy Considerations in Spin-Selective Radical-Ion-Pair Reactions

Iannis K. Kominis

Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective radical-ion pair reactions was introduced most recently, bringing to three the competing theories, including the one traditionally used in spin chemistry. We here consider entropy as a fundamental concept enabling a comparison of the predictions of these theories against what is physically acceptable on quite general grounds.

arXiv:1003.1442•Mar 7, 2010•0 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

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

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

Robert H. Keens, Daniel R. Kattnig

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.

arXiv:2005.04417•New Journal of Physics•Jul 20, 2020•9 citations

Quantum master equations for spin chemistry

Thomas P. Fay

It is a remarkable fact that the interactions between electron and nuclear spins, and their interactions with a magnetic field, can have a profound effect on chemical reactivity, despite the fact that the characteristic interaction energies are orders of magnitude smaller than thermal energy. These observations are explained by the existence of long-lived quantum coherences between spins in certain molecular species (in particular radical pairs), and the study of these spin effects constitutes the field of spin chemistry, a field which spans a wide range of systems, from biochemical reactions to device physics. Because spin chemistry involves subtle quantum effects, many intuitive models used by Physical Chemists, in particular classical kinetic equations, cannot be universally applied. On the other hand, complete first principles modelling of reactions involving spin effects comes at an impossibly high computational cost in complex systems, and often offers little physical insight. In order to address the shortcomings of these approaches, quantum master equations (QMEs) are employed to describe spin chemical phenomena. These are equations that describe a reduced set of degrees of freedom quantum mechanically, accounting for the effects of remaining degrees freedom implicitly. In this thesis I explore the use of QME techniques to resolve a range of problems in spin chemistry. These techniques can be used to obtain the correct radical pair spin QME, resolving questions about the role of quantum measurement in these systems. As well as aiding the development of the theory of spin chemistry, QMEs provide a practical tool for modelling radical pair reactions including spin relaxation effects, as I also demonstrate. As a final study of QME techniques in spin chemistry, I use these methods to show when the classical kinetic description of radical pair reactions is and is not valid.

•Jan 1, 2020•0 citations

Quantum Dynamics of Radical-Ion-Pair Reactions

Iannis K. Kominis

Radical-ion-pair reactions were recently shown to represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts, casting doubt on the validity of the theoretical treatment of these reactions and the results thereof that has been at the core of spin chemistry for several decades now. The ensued scientific debate, although exciting, is plagued with several misconceptions. We will here provide a comprehensive treatment of the quantum dynamics of radical-ion-pair reactions, generalizing our recent work and elaborating on the analogy with the double-slit experiment having partial "which-path" information. This analogy directly leads to the general treatment of radical-ion pair reactions covering the whole range between the two extremes, that of perfect singlet-triplet coherence and that of complete incoherence.

arXiv:1009.2809•Sep 14, 2010•0 citations
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.
Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective radical-ion pair reactions was introduced most recently, bringing to three the competing theories, including the one traditionally used in spin chemistry. We here consider entropy as a fundamental concept enabling a comparison of the predictions of these theories against what is physically acceptable on quite general grounds.
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.
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.
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.
It is a remarkable fact that the interactions between electron and nuclear spins, and their interactions with a magnetic field, can have a profound effect on chemical reactivity, despite the fact that the characteristic interaction energies are orders of magnitude smaller than thermal energy. These observations are explained by the existence of long-lived quantum coherences between spins in certain molecular species (in particular radical pairs), and the study of these spin effects constitutes the field of spin chemistry, a field which spans a wide range of systems, from biochemical reactions to device physics. Because spin chemistry involves subtle quantum effects, many intuitive models used by Physical Chemists, in particular classical kinetic equations, cannot be universally applied. On the other hand, complete first principles modelling of reactions involving spin effects comes at an impossibly high computational cost in complex systems, and often offers little physical insight. In order to address the shortcomings of these approaches, quantum master equations (QMEs) are employed to describe spin chemical phenomena. These are equations that describe a reduced set of degrees of freedom quantum mechanically, accounting for the effects of remaining degrees freedom implicitly. In this thesis I explore the use of QME techniques to resolve a range of problems in spin chemistry. These techniques can be used to obtain the correct radical pair spin QME, resolving questions about the role of quantum measurement in these systems. As well as aiding the development of the theory of spin chemistry, QMEs provide a practical tool for modelling radical pair reactions including spin relaxation effects, as I also demonstrate. As a final study of QME techniques in spin chemistry, I use these methods to show when the classical kinetic description of radical pair reactions is and is not valid.
Radical-ion-pair reactions were recently shown to represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts, casting doubt on the validity of the theoretical treatment of these reactions and the results thereof that has been at the core of spin chemistry for several decades now. The ensued scientific debate, although exciting, is plagued with several misconceptions. We will here provide a comprehensive treatment of the quantum dynamics of radical-ion-pair reactions, generalizing our recent work and elaborating on the analogy with the double-slit experiment having partial "which-path" information. This analogy directly leads to the general treatment of radical-ion pair reactions covering the whole range between the two extremes, that of perfect singlet-triplet coherence and that of complete incoherence.