The effects of static quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent harmonic frequency: Perturbative analysis and numerical calculations
- Indian Association for the Cultivation of Science, Calcutta (India)
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{sub t}. However, it depends upon the rate at which K{sub 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{sub 0} time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 478451
- Journal Information:
- International Journal of Quantum Chemistry, Journal Name: International Journal of Quantum Chemistry Journal Issue: 6 Vol. 54; ISSN IJQCB2; ISSN 0020-7608
- Country of Publication:
- United States
- Language:
- English
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