Effects of dissipation on nonlinearity in transport: Evolution and integrability properties in a molecular dimer

Abstract

The effects of dissipation on the transport of quasiparticles obeying the nonlinear discrete Schr\"odinger equation are studied. Dissipation is introduced via the standard stochastic Liouville equation and, for a molecular dimer, a closed integro-differential equation is derived for the time dependence of the probability difference at the two molecular sites. The equation is solved numerically in the general case and analytically in a certain limit involving weak nonlinearity and damping, and the solutions are used to describe the scattering spectrum. The integrability of the equations of motion is investigated and it is shown that the equations of motion do not possess the Painlev\'e property.