Driven damped quantum harmonic oscillator

Here, t/(f) is the reduced time evolution operator of the driven damped quantum harmonic oscillator. Recall that representation II was used in preceding treatments, taking into account the indirect damping of the hydrogen bond. After rearrangements, the autocorrelation function (45) takes the form [8]... [Pg.256]

Thermal Average of the Translation Operator The Driven Damped Quantum Harmonic Oscillator Quantum Representation II ... [Pg.247]

Another possibility is to extract the reduced time evolution operator from the analytical solution obtained by Louisell and Walker for the reduced time-dependent density operator of a driven damped quantum harmonic oscillator. [Pg.292]

Consequently, the reduced IP time-evolution operator of the driven damped quantum harmonic oscillator takes the form ... [Pg.293]

In this last equation, the right-hand side matrix elements are those of the IP time evolution operator of the driven damped quantum harmonic oscillator describing the H-bond bridge when the fast mode is in its first excited state ... [Pg.317]

From this viewpoint, which is the most fundamental, the line shape as a whole is the sum of the diagonal matrix elements of the time evolution operator of the driven damped quantum harmonic oscillator in the IP representation with respect to the diagonal part of the Hamiltonian of this oscillator. According to Eq. (120), each diagonal element is a sum of time-dependent terms... [Pg.317]

It may be observed that the two Hamiltonians (269) are those of quantum harmonic oscillators, whereas Hamiltonian (270) is that of a driven damped quantum harmonic oscillator, and Hamiltonians (271) are those of driven undamped quantum harmonic oscillators perturbed by the Davydov coupling... [Pg.351]

APPENDIX I THE DRIVEN DAMPED QUANTUM HARMONIC OSCILLATOR... [Pg.418]

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