Structure of the Rate Kernel

The formal linear response analysis of rate coefficient expressions that was carried out in Section V can also be applied to this model of the reacting liquid. Now, however, the starting point of the analysis is the pseudo-Liouville equation (6.1). The lack of time reversal symmetry has important implications, which we shall now discuss. 

In the course of the calculation in Section V, we used the fact that 5n (k)5 (-k) =0, which follows because and 8n have opposite parity under time reversal. As a consequence of the different evolution operators for i 0 and r 0, the foregoing result is no longer true. Therefore we briefly sketch the modification in the results of Section V. 

Starting from the pseudo-Liouville equation for the solute density fields 

The lack of time reversal symmetry manifests itself by the appearance of a 

The dynamic contribution to the damping matrix is also slightly modified because now appears. We have 

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If the reaction can not be modeled by an impulsive collision event, as for atomic recombination or some isomerization reactions, then is zero by time reversal symmetry as discussed earlier. Nevertheless, the structure of the rate kernel has the same qualitative structure as described above. To... 

If we wish to examine only the structure of the rate kernel, we know that it is sufficient to study the decay of fluctuations about equilibrium. If we let... 

Before closing this section, we should remark that although this analysis of velocity relaxation effects has focused on a simple collision model, we expect that the detailed structure of the rate kernel for short times will depend on the precise form of the chemical interactions in the system under consideration. It is clear, however, that a number of fundamental questions need to be answered before more specific calculations can be undertaken form the kinetic theory point of view. 

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