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We investigate the time evolution process of one selected (initially preparedby optical pumping) vibrational molecular state, coupled to all otherintra-molecular vibrational states of the same molecule, and also to itsenvironment. Molecular states forming the first reservoir are characterised bya discrete dense spectrum, whereas the environment reservoir states form acontinuous spectrum. Assuming the equidistant reservoir states we find theexact analytical solution of the quantum dynamic equations. System reservoirscouplings yield to spontaneous decay of the states, whereas system-reservoirexchange leads to recurrence cycles and Loschmidt echo and double resonances atthe interlevel reservoir transitions. Due to these couplings the system $S$time evolution is not reduced to a simple exponential relaxation. We predictvarious regimes of the system dynamics, ranging from exponential decay toirregular damped oscillations. Namely, we show that there are four possibledynamic regimes of the evolution: (i) - independent of the environmentexponential decay suppressing backward transitions, (ii) Loschmidt echo regime,(iii) - incoherent dynamics with multicomponent Loschmidt echo, when the systemstate exchanges its energy with many states of the reservoir, (iv) - cyclemixing regime, when the long term system dynamics appear to be random. Wesuggest applications of our results for interpretation of femtosecond vibrationspectra of large molecules and nano-systems.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

New mechanism for non-trivial intra-molecular vibrational dynamics