Quantum effects in intermediate-temperature dipole-dipole correlation-functions in the presence of an environment

We study thermal dipole-dipole correlation functions and their corresponding IR spectra in the presence of an intermediate temperature bath of harmonic oscillators. Whereas for a Morse oscillator without coupling to a heat bath, the quantum level structure is displayed in the spectrum, classical calculations show a broad, smeared out spectrum. In the presence of purely Ohmic dissipation already for extremely weak relaxation rate, the classical case is recovered. Using the HEOM approach of Tanimura and Wolynes [Phys. Rev. A 43, 4131 (1991)], we show that to observe some remnants of the level structure in the spectrum for moderate damping strength as well as intermediate temperatures, the dynamics has to be non-Markovian (Ohmic dissipation with cutoff).