The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.
The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.
Radical pairs are short-lived, spin-correlated intermediates that underpin processes in chemistry, biology, and emerging quantum technologies. Their behavior is governed by coupled electron-nuclear spin dynamics and is sensitive to weak magnetic fields, but full quantum treatments have been obstructed by the extreme computational cost of modeling many interacting spins. Here, this barrier is removed, demonstrating that open-system radical-pair dynamics can be resolved at nuclear-spin scales previously intractable, explicitly reaching regimes with tens of coupled nuclei and validated up to 60 spins. In biologically relevant flavin-tryptophan radical pairs, electron-transfer pathways and magnetic-field anisotropy are found to reshape spin evolution and, in turn, spin-selective reaction yields. The resulting directional responses expose a strong mechanistic link between the nuclear environment, magnetic geometry, and chemical outcome-a relationship central to hypotheses of avian magnetoreception and other magnetic-field effects in biology. This establishes a widely applicable simulation framework that removes a long-standing barrier in spin chemistry, quantum biology, and spin-based device science.
Radical pairs and the dynamics they undergo are prevalent in many chemical and biological systems. Specifically, it has been proposed that the radical-pair mechanism results from a relatively strong hyperfine interaction with its intrinsic nuclear spin environment. While the existence of this mechanism is undisputed, the nanoscale details remain to be experimentally shown. Here, we analyze the role of a quantum sensor in detecting the spin dynamics (non-Markovian) of individual radical pairs in the presence of a weak magnetic field. We show how quantum control methods can be used to set apart the dynamics of the radical-pair mechanism at various stages of the evolution. We expect these findings to have implications to the understanding of the physical mechanism in magnetoreception and other biochemical processes with a microscopic detail.
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.
Quantum biology is now taken rather seriously. Photosynthesis and avian navigation are two key applications of quantum biology. The basic problem in both cases is posed by the fact that the magnetic interaction energy in Earth's magnetic field is roughly million times smaller than thermal energy. The so called radical-pair mechanism (RPM) was proposed already in the 60's as a possible solution to the problem posed by anomalously large effect in EPR and NMR experiments. According to RPM, a radical pair is accompanied by electron pair, which is in a superposition of spin triplet and singlet states and behaves as quantum coherent system for a time sufficiently long to induce chemical effects. The hyperfine interaction of the members of the electron pair with the nuclei of radicals would amplify the effect. The neutralization of radical pair puts an end to the coherence interaction period. The proposal is that RPM gives rise to chemical compass making possible avian navigation. There is however a problem. RPM has been observed in laboratory only for magnetic fields in the range 1 mT-10 T. Earth's magnetic field is only 2 per cent of the lower bound so that it is quite possible that RPM is not at work. This opens up the door for new quantum physics proposed by TGD based model of quantum biology. In this approach magnetic body acts as as intentional agent using biological body as a sensory receptor and motor instrument. Macroscopic quantum coherence is made possible by dark matter realized as a hierarchy of heff = n x h phases. In this article RMP is summarized and compared with the TGD based vision. Also the possible connection between avian navigation and circadian clock suggested by the fact that both involve photoreceptor known as cryptocrome and a possible connection with gravitaxis are considered in TGD framework.
The Radical Pair Mechanism, a process by which magnetic fields modulate the kinetics of chemical reactions by influencing spin dynamics, is thought to underlie a variety of biological mechanisms and is inherently both quantum and noisy. Model simulations with limited electron-nuclear interactions have been conducted on classical devices resulting in experimentally verified final state results, however these simulations become too complex to simulate as the systems scale in size. This motivates us to propound the simulation of the relevant spin dynamics in a noisy quantum device to probe the currently unexplored open quantum systems aspects of the radical pair mechanism and to provide a novel theoretical tool for us to be able to tackle bottlenecks in simulating larger and more physically relevant biological spin systems. We employ a hybrid quantum machine learning approach where we evaluate a parametrized quantum circuit representing the evolution of the system on the quantum device and then update the parameters according to our objective cost function on a classical computer using a gradient optimizer and a noisy gradient free (SPSA) optimizer. We show that a 3 qubit circuit with a series of parametrized rotation gates representing the Hyperfine and Zeeman interactions can be optimized, resulting in a circuit that evolves a singlet state under different magnetic field angles. Moreover, we show that the noisy gradient free optimizer is better suited for optimizing on a noisy quantum device. However, the precision in the quantum circuit outputs is only sub-par at present, leaving room for further improvements.
The radical pair mechanism (RPM) is a quantum-chemical mechanism that relates magnetic fields to the spin states of a pair of electrons, thereby affecting their availability for chemical reactions. The mathematics of electron spin and magnetic fields can be discouragingly complex. However, if biological systems can be assumed to respond to at most a subset of an electron’s spin state prior to that spin state being randomized, the relevant mathematics simplifies. A construction of the RPM under that assumption is developed step by step. A single electron is examined first, where a common representation of an electron’s spin state using the surface of a sphere is reduced to a line. A uniform magnetic field is then added. Next, an electron pair is examined, with the spin of each electron represented using a unit circle and the spin of the pair by a torus. Entanglement is represented by a probability distribution over the surface of the torus. Iwo magnetic fields are added, completing the construction of the RPM; the effect of magnetic fields on energy levels are also discussed. The resulting construction illuminates various aspects of the singlet (S0) and triplet (T+, T0, T-) states, though also has certain limitations, which are discussed.