  The exciton relaxation dynamics of photoexcited electronic states in
poly($p$-phenylenevinylene) (PPV) are theoretically investigated within a
coarse-grained model, in which both the exciton and nuclear degrees of freedom
are treated quantum mechanically. The Frenkel-Holstein Hamiltonian is used to
describe the strong exciton-phonon coupling present in the system, while
external damping of the internal nuclear degrees of freedom are accounted for
by a Lindblad master equation. Numerically, the dynamics are computed using the
time evolving block decimation (TEBD) and quantum jump trajectory techniques.
The values of the model parameters physically relevant to polymer systems
naturally lead to a separation of time scales, with the ultra-fast dynamics
corresponding to energy transfer from the exciton to the internal phonon modes
(i.e., the C-C bond oscillations), while the longer time dynamics correspond to
damping of these phonon modes by the external dissipation. Associated with
these time scales, we investigate the following processes that are indicative
of the system relaxing onto the emissive chromophores of the polymer: 1)
Exciton-polaron formation occurs on an ultra-fast time scale, with the
associated exciton-phonon correlations present within half a vibrational time
period of the C-C bond oscillations. 2) Exciton decoherence is driven by the
decay in the vibrational overlaps associated with exciton-polaron formation,
occurring on the same time scale. 3) Exciton density localization is driven by
the external dissipation, arising from `wavefunction collapse' occurring as a
result of the system-environment interactions. Finally, we show how
fluorescence anisotropy measurements can be used to investigate the exciton
decoherence process during the relaxation dynamics.
