It is no surprise, therefore, that the mapping to a Markov diffusion process which underlies this work has precedents in the physical and mathematical literature: it is the foundation of Nelson's "stochastic" formulation of quantum mechanics \cite{Nelson_1966} and has be used to study tunnelling phenomena \cite{Yasue_1978}
In the opposite direction (from a Markov process to a Hamiltonian operator), the transformation is a classical trick to solve Fokker-Planck equations 
The value of these analogies is twofold. First, they bring the large repertoire of results and techniques derived in quantum many-body theory and condensed matter physics to bear on evolutionary dynamics. For instance, since the quasispecies distribution \(\)\(Q\) is the ground state of a disordered quantum Hamiltonian, we can use the forward scattering approximation familiar from Anderson and many-body localization theory \cite{Pietracaprina_2016} to compute the effective potential \(U\) in the small \(\mu\) limit; this gives good results, see Fig. XXX. Among the non-perturbative approaches which directly applicable to the dynamical analysis of fitness landscapes are quantum Monte Carlo methods; in particular, diffusion Monte Carlo techniques \cite{Kosztin_1996} are directly based on the linearized Crow-Kimura equation (known in this context as the Schrödinger equation in imaginary time). 
The second reason \(Q\)