Resummation technique

In an earlier work we performed a quantum calculation using the exponential resummation technique and found results that agreed qualitatively with those of Azzouz and Borgis. When we allowed for a position-dependent friction, we obtained a function g(s) that is plotted in Fig. 2. The results for the quantum rate are presented in Tables II and 111. The column g(s) = s refers to the position-independent case, as calculated in our earlier work on this system. 

Clearly, there is a great deal of scope for further studies of convergence aspects of the QNF as well as related optimal truncation and resummation techniques. 

It has been shown that the series (2.100) is asymptotic, and suffers from an explosive increase in its coefficients which increase roughly like n . However, by an appropriate resummation technique, usefiil information can be drawn about the asymptotic behaviour of large In particular, the exponent v is estimated as ... 

In the next section we will discuss recent computer studies of time correlation functions for dense gases that also provide a striking confirmation of the resummation techniques discussed here. 

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