Bang, Ole2; Christiansen, Peter Leth3; If, F.4; Rasmussen, Kim1; Gaididei, Y. B.5
1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Photonics Engineering, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Technical University of Denmark5 Bogolyubov Institute for Theoretical Physics
A nonlinear dynamical model of molecular monolayers arranged in Scheibe aggregates is derived from a proper Hamiltonian. Thermal fluctuations of the phonons are included. The resulting equation for the excitons is the two dimensional nonlinear Schrodinger equation with noise. Two limits of the complicated spectrum of the noise are considered: time independent, spatially white noise, simply corresponding to disorder in the arrangement of the molecules, and pure white noise. Parameter values are found by comparison with experiments by Mobius and Kuhn [Isr. J. Chem. 18, 375 (1979)] and order of magnitude estimates given where experiments are not available. The temperature dependent coherence time is found from numerical simulations. Experiments show that the excitons stay coherent during their life-time. This is in correspondence with the model at temperatures lower than 3 K. To increase this limiting temperature it is found that the dipole-dipole coupling and the exciton-phonon coupling must be decreased significantly.
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 1994, Vol 49, Issue 5, p. 4627-4636