White Noise and Nonlinear Damping in the Two-Dimensional Model of Energy Transfer in Molecular Systems

Abstract

In the present paper a model of energy transfer in Langmuir-Blodgett Scheibe aggregates which takes into account the non-vanishing thermal fluctuations in molecular systems is derived. This is done using the two-dimensional NLS equation with multiplicative noise, which describes the exciton coherence destruction caused by phonons and providing energy input to the exciton system, and with nonlinear damping providing energy dissipation. Using a collective coordinate approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead result in an exponentially decreasing width of the solution in the long-time limit. We also find that a sufficiently large noise variance may cause an initially localized distribution to spread instead of contracting, and that the critical variance necessary to cause dispersion will for small damping be the same as for the undamped system.