THE EFFECTS OF STATIC QUARTIC ANHARMONICITY ON THE QUANTUM DYNAMICS OF A LINEAR OSCILLATOR WITH TIME-DEPENDENT HARMONIC FREQUENCY - PERTURBATIVE ANALYSIS AND NUMERICAL CALCULATIONS

摘要

The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (omega) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2,4,6...) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (lambda), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the lambda profile is independent of the specific form of the time dependence of the force constant, K-f. However, it depends upon the rate at which K-t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H-0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensify oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. (c) 1995 John Wiley and Sons, Inc. [References: 22]