Zero-temperature fluctuation-dissipation

The starting point for the proposed new approach is an exact formula [238], [239], based on the adiabatic connection formula and the zero-temperature fluctuation-dissipation theorem, relating the groundstate xc energy to the inter-... 

At temperatures above Tc there is no instanton, and escape out of the initial well is accounted for by the static solution Q = Q with action SeU = /3V0 (where V0 is the adiabatic barrier height here) which does not depend on friction. This follows from the fact that the zero Fourier component of K(t) equals zero hence the dissipative term in (5.39) vanishes if Q is constant. The dissipative effects come about only through the prefactor that arises from small fluctuations around the static solution. Decomposing the trajectory into a Fourier series... 

This equation gives the mean-square value of the voltage appearing across the terminals of a capadtor filled with a dielectric of zero-frequency relative permittivity, s in terms of Co, the capacitance without a dielectric, and the absolute temperature, T. This noise voltage is caused by the thermally induced dipole-moment fluctuations which are themselves inextricably bound up with the dissipative processes. That this is so is indicated by the fact that equation (42) applied to aJ,to) leads to the relation... 

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