Abstract
The time correlation function\(\dot \chi\)(t)=Re<[c(t), c †(0)]>, which is related to the dipole spectrum and is the main focus of quantum molecular time scale generalized Langevin equation theory, is calculated for the Hamiltonian system in which a single oscillator is coupled by a nonlinear Davydov term to a chain of oscillators comprising a phonon heat bath. An exact expression for\(\dot \chi\)(t) is obtained. At long times we find that the time correlation function decays as a small power law atT=0K, but switches to exponential decay at higher temperature. This is a new result and bears on the long-standing issue of the existence of long-time tails.
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McDowell, H.K., Clogston, A.M. Exact time correlation function for a nonlinearly coupled vibrational system. J Stat Phys 67, 331–346 (1992). https://doi.org/10.1007/BF01049038
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DOI: https://doi.org/10.1007/BF01049038