Path integral influence functional theory of dynamics of coherence between vibrational states of solute in condensed phase

Abstract

Path integral influence functional theory has been applied to the dynamics of coherence between vibrational states of solute in condensed phase. First, time evolution of the off-diagonal term of the reduced density matrix rho(mn)(t) was algebraically described by the cumulant expansion of the perturbative influence functional. Then, the theory is compared with the Redfield theory, rearranging the present description in a familiar way to that found in the Redfield theory. A numerical example of the theory is presented for the vibrational dynamics of cyanide ion in water assuming a coherent state (1/radical2)(|0> + |1>) at t = 0. We find that Re rho(10)(t) oscillates with high frequency and shows a fast damping. Relaxation time of the oscillation amplitude is estimated to be 5.1 ps for a certain configuration of the solution. Then, secular approximation often used in the Redfield theory is found to work well, at least, in the present system. Population relaxation time for the first excited state and pure dephasing time may also be calculated from the component of Re rho(10)(t) to be 7.9 and 7.5 ps, respectively. Further, the many-particle measurement for Re rho(10)(t) gives the relaxation rate about three times faster than the single-measurement above. This comes from the inhomogeneity of the solute environment. We also found the fast oscillation in the diagonal part of the calculated density matrix, Re rho(11)(t). This oscillation is generated only when the initial density matrix includes the coherence.