Influence of a phonon bath on electronic correlations and optical response in molecular aggregates

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Axt, Vollrath Martin ; Mukamel, Shaul:
Influence of a phonon bath on electronic correlations and optical response in molecular aggregates.
In: Moloney, Jerome V. (ed.): Nonlinear Optical Materials. - Berlin ; New York : Springer , 1998 . - pp. 1-32 . - (The IMA Volumes in Mathematics and its Applications ; 101 )
ISBN 0-387-98581-6
DOI: https://doi.org/10.1007/978-1-4612-1714-5_1

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A generating function algorithm that allows the calculation of the optical response of coupled exciton-phonon systems is developed. For a model of assemblies of three-level molecules coupled via dipole interaction and interacting linearly with nuclear degrees of freedom, we derive a closed set of equations of motion for five generating functions representing the exact response to third order in the external field. These are equivalent to an infinite hierarchy of equations of motion for phonon-assisted variables. Starting with the equations for the generating functions, several reduction schemes are derived. By eliminating the phonon degrees of freedom in favor of self-energies, the Haken-Strobl model of relaxation is recovered as a limiting case. A set of time-local equations is presented extending the Haken-Strobl treatment by keeping the temperature dependence as well as the excitonic signatures of the phonon self-energies. Finally, we derive equations that interpolate between the coherent and incoherent limits of exciton propagation and properly include the two exciton dynamics.