Significance of the response matrix

The response matrix II, defined in (12.3.23) and (12.3.24), enables us to find the time-dependent change in the expectation value of any quantity, B say, as the result of a perturbation (12.3.16) containing the operator A. It therefore yields an approximation to the FDP /T(BA oj) defined formally in Section 12.1. 

The symmetry properties of the FDPs, noted in Section 12.1, are reflected in those of the response matrix. Thus the n matrix that appears 

On putting the row and column submatrices of (12.4.3) in reverse order and taking the complex conjugate (noting the property (12.3.20)), we then obtain, from (12.4.4), 

The two terms in (12.4.2) are therefore complex-conjugate, and the fluctuation d(B) is real. 

The effect of the ie term is revealed when we consider the time variation 6(B) resulting from the perturbation 

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