We investigate the time evolution process of one selected (initially prepared
by optical pumping) vibrational molecular state, coupled to all other
intra-molecular vibrational states of the same molecule, and also to its
environment. Molecular states forming the first reservoir are characterised by
a discrete dense spectrum, whereas the environment reservoir states form a
continuous spectrum. Assuming the equidistant reservoir states we find the
exact analytical solution of the quantum dynamic equations. System reservoirs
couplings yield to spontaneous decay of the states, whereas system-reservoir
exchange leads to recurrence cycles and Loschmidt echo and double resonances at
the interlevel reservoir transitions. Due to these couplings the system S
time evolution is not reduced to a simple exponential relaxation. We predict
various regimes of the system dynamics, ranging from exponential decay to
irregular damped oscillations. Namely, we show that there are four possible
dynamic regimes of the evolution: (i) - independent of the environment
exponential decay suppressing backward transitions, (ii) Loschmidt echo regime,
(iii) - incoherent dynamics with multicomponent Loschmidt echo, when the system
state exchanges its energy with many states of the reservoir, (iv) - cycle
mixing regime, when the long term system dynamics appear to be random. We
suggest applications of our results for interpretation of femtosecond vibration
spectra of large molecules and nano-systems.Comment: 11 pages, 2 figure
