Generalized master equations from the nonlinear Schrödinger equation and propagation in an infinite chain

Abstract

Generalized master equations with nonlinear memory functions describing quasiparticle transport on lattices are derived explicitly from the discrete nonlinear Schr\"odinger equation through the application of diagonalizing projection operators. Exact results are presented for dimers, and an approximation scheme is developed for extended systems such as an infinite chain, which treats the nonlinearity exactly and the intersite transfer perturbatively. An apparent connection to the Toda lattice is pointed out. The exact results presented for the dimer include an explicit evaluation of the initial (driving) term in the generalized master equation.