Role of the Bath Spectrum in the Specific Heat Anomalies of a Damped Oscillator

The specific heat anomalies are analytically studied in the system in which a harmonic oscillator couples to a heat bath with harmonic noise. The physical explanation leads to a general spectral dependence of the specific heat anomalies. The condition of a dip appearance and the behaviors of the dip can be given according to the shape of the bath's power spectrum by employing the minimal heat bath model.