Suppose that 
is of the form
which adiabatically induces a fluctuation in the system for t;SPMlt;0 and the lets the
system evolve in time according to the unperturbed Hamiltonian for t;SPMgt;0.
How will the induced fluctuation evolve in time? Combining the kubo transform
relation with the linear response result for 
, we find that
where the change of variables u=t-s has been made. Taking the limit 
,
and performing the integral over u, we find
Since we assumed that 
, we have 
. Thus, dividing by
, we find
Thus at long times in the classical limit, the fluctuations decay to 0, indicting a complete regression or suppression of the induced fluctuation:
