The dynamics of coherent wave packets in a medium with memory

Two qualitatively different approaches to the description of the dynamics of vibrational wave packets, with and without (Markovian approximation) taking into account memory of relaxation processes, were compared for a model molecular system with one vibrational degree of freedom (a Morse oscillator) in a medium. The master equation for the density matrix of the molecular system obtained using the Nakajima-Zwanzig formalism was used. The time evolutions of the autocorrelation function, vibrational level populations, and mean vibrational wave packet energies were calculated. At short times, taking memory effects into account could cause significant quantitative and sometimes qualitative differences in the evolution of vibrational wave packets calculated in the Markovian approximation.