A reduced set of exact equations of motion for a non-number-conserving Hamiltonian (Q1403435)

The Davydov model for energy transfer in proteins is extended to describe situations in which the excitation number is not conserved. While the full state of the system consists of an infinite superposition of states with all possible excitation numbers, we derive a complete set of differential equations for a reduced number of variables of the system. For a system with \(N\) sites, the number of variables needed to represent the full state varies as \(m^N\), \(m\) being an a priori defined maximum excitation number, whereas the number of equations in our reduced system grows as \(N^2\). The solutions of the reduced set of equations not only allow for the determination of quantities such as the energies of the different components of the system, but constitute also an important reference for the full equations of motion.