For a closed quantum system, a dynamical invariant is defined as an operator whose expectation value is a constant. In this paper, we extend the concept of dynamical invariants from closed systems to open systems. A dynamical equation for invariants (the dynamical invariant condition) is derived for Markovian dynamics. Different from dynamical invariants of closed quantum systems, the time evolution of dynamical invariants of open quantum systems is no longer unitary, and eigenvalues of any invariant are time-dependent in general. Since any hermitian operator which can fulfill the dynamical invariant condition is a dynamical invariant, we construct a type of special dynamical invariants of which a part of the eigenvalues is still constant. The dynamical invariants in the subspace spanned by these eigenstates thus evolve unitarily.

Primitive photosynthetic cells appear over three billion years prior to any other more complex life-forms, thus it is reasonable to assume that Nature has designed a photosynthetic mechanism using minimal resources but honed to perfection under the action of evolution. A number of different quantum models have been proposed to understand the high degree of efficient energy transport, most of them are limited to the scenario of single-exciton. Here we present a study on the dynamics in light-harvesting complexes beyond the single exciton limit, and show how this model describes the energy transfer in the Fenna-Matthew-Olson (FMO) complex. We find that the energy transfer efficiency above 90% under realistic conditions is achievable.