Entangled and dark stationary states of excitation energy transport models in quantum many-particle systems and photosynthesis

We characterize the stationary states of an excitation energy transfer model in quantum many-particle systems [Y. Aref’eva, I. Volovich and S. Kozyrev, Stochastic limit method and interference in quantum many-particles systems, Theor. Math. Phys. 183(3) (2015) 782–799] as well as the stationary states of a quantum photosynthesis model [S. Kozyrev and I. Volovich, Dark states in quantum photosynthesis, arXiv:1603.07182v1 [physics.bio-ph]] in terms of a transport operator. It turns out that, apart from the ground state, all invariant states of the excitation energy transport model are entangled. For the photosynthesis model, any invariant state in the commutant of the system Hamiltonian is a mixed bright–dark state in the sense of [S. Kozyrev and I. Volovich, Dark states in quantum photosynthesis, arXiv:1603.07182v1 [physics.bio-ph]] and it is pure dark if and only if the bright vector belongs to the kernel of this state.