Correlation functions classical bath models

Consider first the model described by Eqs (13.6), (13.7), (13.10), and (13.11) where the hannonic oscillator under study is coupled bi-linearly to the harmonic bath. The relevant correlation functions ( F(Z),.F(0) ) and (F(Z)F(0))c should be calculated with F = and its classical countei part, where Uj are coordin-... 

Such correlation functions are often encountered in treatments of systems coupled to their thermal environment, where the model for the system-bath interaction is taken as a product of or S with a system variable. In such treatments the coefficients Cj reflect the distribution of the system-bath coupling among the different modes. In classical mechanics these functions can be easily evaluated explicitly from the definition (6.6) by using the general solution of the harmonic oscillator equations of motion... 

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