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Chemical Physics Letters

Dynamics of a morse oscillator coupled to a bath of harmonic oscillators

Mingwhei Tung, Elia Eschenazi, Jian‐Min Yuan

Published Apr 1, 1985• 5 citations
Publisher
DOI
10.1016/0009-2614(85)85158-7

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In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.
We have studied by using quantum mechanics the dynamics of a driven damped Morse oscillator, whose classical solutions exhibit bistable and chaotic behavior. In this treatment the Morse Hamiltonian, expressed in terms of the generators of an su(2) algebra, is coupled to a bath of harmonic oscillators and driven by a classical field, simulating an infrared laser. We have derived the generalized master equation from the Liouville equation within the Markoffian and weak‐coupling approximation. The time dependence of the average energy of the Morse oscillator is obtained by solving the time evolution equations for the matrix elements numerically as a function of the relaxation times, laser amplitude and frequency. Bistability does not show up as a hysteresis loop in the quantum solution, but as a bimodal population distribution in vibrational energy levels. As the field amplitude increases the time series of the average Morse energy becomes increasingly irregular.
We report the first numerical calculations in which converged Matsubara dynamics is compared directly with exact quantum dynamics with no artificial damping of the time-correlation functions (TCFs). The system treated is a Morse oscillator coupled to a harmonic bath. We show that, when the system-bath coupling is sufficiently strong, the Matsubara calculations can be converged by explicitly including up to M = 200 Matsubara modes, with the remaining modes included as a harmonic "tail" correction. The resulting Matsubara TCFs are in near-perfect agreement with the exact quantum TCFs, for non-linear as well as linear operators, at a temperature at which the TCFs are dominated by quantum thermal fluctuations. These results provide compelling evidence that incoherent classical dynamics can arise in the condensed phase at temperatures at which the statistics are dominated by quantum (Boltzmann) effects, as a result of smoothing of imaginary-time Feynman paths. The techniques developed here may also lead to efficient methods for benchmarking system-bath dynamics in the overdamped regime.