Dynamics of Radiationless Transitions in Large Molecules: 2. Recurrence Cycles in Population Evolution of the Initial State

Evolution of the population of the initial state S is due to radiationless transitions into a dense discrete spectrum of intramolecular vibrations {R-n} (reservoir R) and spontaneous decay of S and R-n by virtue of coupling with a continuous spectrum of intermolecular vibrations (reservoir Q). An exact solution to the dynamic problem has been found, which indicates that in contrast to the Fermi approximation, which reproduces only the exponential decay of S, the evolution consists of recurrence cycles such that Loschmidt echo (partial recovery of the population of S via back transitions from R-n) appears in each cycle. The width and number of echo components depend upon average characteristics of the spectrum of R. With an equidistant spectrum and the same coupling constants of S with all R states, the decay of S is exponential in the initial cycle and the number of echo components and echo width increase proportionally to the cycle number in subsequent cycles. The increase in the width causes mixing of the echo components and the transition from regular to quasi-stochastic dynamics. Deformation of the equidistant spectrum leads to nonexponential decay in the initial cycle, an increase in the number of components, and a reduction in the number of cycles with regular dynamics.