Symmetrized correlation function

To get a classical limit, the symmetrized correlation function is represented by ... 

It will also be useful to define the symmetrized correlation function C(t) ... 

The Dissipative Part of the Response Function in Terms of the Symmetrized Correlation Function... 

The symmetrized correlation function of the random force, namely the function Cff(t, t ) as defined by... 

The expression of the symmetrized correlation function in terms of the dissipative part of the response function can be derived, in like manner (i.e., by using contour integration), or by inverting the convolution equation (38). Thus we compute on the contour T (Fig. 1) the integral... 

Before entering the discussion of the classical limit, we will propose another formulation of the FDT as given by Eq. (37) or Eq. (38) in the time-domain. It provides the expression of the dissipative part of the linear response function in terms of the derivative of the symmetrized correlation function, an expression which becomes particularly simple in the classical limit [34]. 

We now turn to quantum Brownian motion as described by the generalized Langevin equation (22), with the symmetrized correlation function of the random force as given by Eq. (20). 

In studying uniaxially deformed polymers, we can confine ourselves to systems with cylindrically symmetric correlation functions. It should be recognized that this does not impose any symmetry on the electron density distribution Q (X). Introducing cylindrical coordinates (x, X3, x ) and (s S3, s,) and integrating over the azimutal angles x, and s. Equations (27) and (28) become... 

Valuable information on crazes can be derived from their scattering behavior at large values of s. Following a derivation given by Porod it may be shown that a two-phase system with sharp phase boundaries and a cylindrically symmetric correlation function obeys the asymptotic law... 

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