Intramolecular vibrations and noise effects on pattern formation in a molecular helix

Modulational instability in a biexciton molecular chain is addressed. We show that the model can be reduced to a set of three coupled equations: two nonlinear Schrödinger equations and a Boussinesq equation. The linear stability analysis of continuous wave solutions of the coupled systems is performed and the growth rate of instability is found numerically. Simulations of the full discrete systems reveal some behaviors of modulational instability, since wave patterns are observed for the excitons and the phonon spectrum. We also take the effect of thermal fluctuations into account and we numerically study both the stability and the instability of the plane waves under 300K. The plane wave is found to be stable under modulation, but displays a gradual increase of the wave amplitudes. Under modulation, the same behaviors are observed and wave patterns are found to resist thermal fluctuations, which is in agreement with earlier research on localized structure stability under thermal noise.