Analysis of quantum coherence in biology

First-order interactions between quantum states; the matrix element V describes the strength of the interaction between the state |s> and the set of states {|j>} with the state density ρj. The state energies are characterized by complex values, with the imaginary part describing the respective state width. [Display omitted] •Theoretical methods for quantum coherence dynamics in biology reviewed.•Namely, effective Hamiltonian (EH), Green’s function and density matrix methods.•Quantum coherence dynamics in photosynthesis, brain and vision discussed.•The EH method recommended for interpreting quantum coherence effects in biology. We reviewed the tools of quantum physics used in modeling of quantum coherence (QC) effects in different systems, including biological systems, which behave as quantum objects in some of their degrees of freedom. In particular, we considered the usage of the effective Hamiltonian (EH), Green’s function (GF) and density matrix (DM) methods in the analysis of QC, focusing on QC in biological systems. We discussed the two main mechanisms of loss of quantum state coherence: (i) dephasing of the originally prepared coherent wave package and (ii) population relaxation in the same wave package. Dephasing does not affect the quantum state population, e.g. as in spin-spin relaxation, where dephasing is described by the τ2 relaxation time. On the other hand, the state population relaxation of the spin wavepackage is attributed to spin-lattice relaxation and is described by the τ1 relaxation time. Presently we discussed EH and GF formalisms in terms of the complex energy, dependent on intra- and intersystem interactions that induce state population relaxation. We provided a detailed analysis of these approaches for the exciton relaxation dynamics in a glycine polypeptide chain. The same phenomena were described in the DM formalism using the relaxation matrix. We discussed QC in different biological systems, showing that QC is conserved when the interactions of the coherent wavepackage with other degrees of freedom are weak, as otherwise population relaxation causes loss of QC. We believe that our results will be useful for the researchers in the area of quantum biology.