We introduce a non-Hermitian approximation of Bloch optical equations. Thisapproximation provides a complete description of the excitation, relaxation anddecoherence dynamics of ensembles of coupled quantum systems in weak laserfields, taking into account collective effects and dephasing. In the proposedmethod one propagates the wave function of the system instead of a completedensity matrix. Relaxation and dephasing are taken into account viaautomatically-adjusted time-dependent gain and decay rates. As an application,we compute the numerical wave packet solution of a time-dependent non-HermitianSchrodinger equation describing the interaction of electromagnetic radiationwith a quantum nano-structure and compare the calculated transmission,reflection, and absorption spectra with those obtained from the numericalsolution of the Liouville- von-Neumann equation. It is shown that the proposedwave packet scheme is significantly faster than the propagation of the fulldensity matrix while maintaining small error. We provide the key ingredientsfor easy-to-use implementation of the proposed scheme and identify the limitsand error scaling of this approximation.
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