Instantaneously Dynamical Response and Correlation Functions in Independent-Oscillator Model

For the independent-oscillator model (IOM), the explicit expressions of the instantaneously dynamical response functions (Χ₁ + Υ,t₁), X(t₁ + Υ,t₁)) and correlation functions (φ(t₁ + Υ,t₁)+Φ(t₁ + Υ,t₁)) for both the system and environment are derived. It is shown that for external perturbation the environment of IOM is dynamically stable and the system is oscillatory. Although the external perturbation exists, there is still strongly temporal correlation for the system, for the environment, however, the temporal correlation quickly decays with the second time variable Υ and is almost independent of the first time variable t₁, nevertheless is significantly affected by dissipation. It is shown that the environment behaves as a heat bath from the dynamical point of view.