## 1 Introduction
The complexity of the system has required the use of well-known developments of other disciplines as tentative approaches to the problem. A diagram of the main scientific branches involved in the study of the FMO complex is depicted in Figure 1 remarking just some emblematic works contributing to the understanding of the FMO complex. This map shows the complexity and richness of the problem which should be addressed in the understanding and collaborative research around it. In fact, the first widely studied light-harvesting complex was the FMO pigment-protein. This photosynthetic antenna holds bacteriochlorophyll \(a\) photopigments within its protein scaffold. Bacteriochlorophyll \(a\) (commonly abbreviated as BChl \(a\) but not widely used in this work) is only one type of the different photopigments (also known as chromophores) being present in the majority of anoxygenic photobacteria [4]. These bacteriochlorophylls act as antennas capturing photons and transferring their energy through the complex to the bacteria reaction center. For the reader's ease, in the remaining development of this article, we will be using only the abbreviation BChl as reference to any bacteriochlorophyll \(a\) chromophores in the complex. The FMO complex is found in all species of green sulfur bacteria (see Section 2.1). The study of the FMO complex is a clear example of a multidisciplinary effort to understand its entire behavior departing from its biological role, chemical structure and physical processes involved, among them, the quantum properties of such a biological system. Excitation energy transfer in GSB within the FMO and including other photosynthetic complexes can be pictured as a multi-layer cascade process for transfer of energy first coming from the environmental photons (Figure 2). There, the FMO could be conceived as a multipartite funnel with a spring scaffolding where energy is collected at a top large surface to excite some of its components (the pigments) and then being transferred and concentrated towards a sink, while the process is damped by its scaffolding structure to reboot the FMO. The energy transfer happening in this funnel involves the migration of excited states being sequentially shared by the pigments. In order to bring this analogy closer to reality we must think of this light-harvesting funnel as an arrangement of pigment particles (the BChls) with dipole like charge distributions and springs holding them to the surrounding structure and connecting them to one another. The photons (energy packets) from which the energy is being absorbed and transferred can be visualized as a rain of pebbles from different sizes (their energy or frequency). To know how many photons are absorbed by a pigment particle one must only know the photon flux and the effective cross-sectional area of the pigment [4]. This is not a physical size but rather an effective size considering factors such as the wavelength of excitation. As energy transfer occurs in this system, we can imagine the springs movement causing slight changes to the original arrangement at the time they partially damp the process. It can be understood as the changes in the protein structure as the transfer occurs, which we label as the \"reorganization energy\", \(\lambda\). The driving force for energy transfer is more or less equal but in opposite direction to the reorganization energy [21]. Key quantities  
Figure 1: Schematic map of the multidisciplinary study surrounding the FMO research and some works that have provided the basis of this article. are the electronic coupling between the BChls, the electron-phonon coupling (reorganization energy \(\lambda_{k}\) and time scale \(\gamma_{k}^{-1}\)), the temperature \(T\), and the disorder [21]. Finally, such an energy transfer boosts the reduction/oxidation chemical reactions taking place in the RC, involving other biological components and continuing the photosynthetic process. This loony picture (Figure 2) is useful to capture the general process formally depicted below in a much more technical description.