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In the example given in Sec., the classical dynamics happens to give the correct result at zero time (t=0) for the Kubo-transformed momentum autocorrelation function and thus provides a reasonable prior. We note that the MEAC+classical can still be extended to general autocorrelation functions as well, although one might have to adjust the prior spectrum [i.e., times the ratio C AA quantum (t=0) / C AA classical (t=0)] to obtain the exact value of the correlation function at zero time (t=0). Among all versions of quantum mechanics correlation functions, the Kubo-transformed correlation function is the one which most naturally corresponds to the classical correlation function, so it is reasonable that it provides the best choice to use in Eqs. for the MEAC+classical method.
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In the example given in Sec., the classical dynamics happens to give the correct result at zero time (t=0) for the Kubo-transformed momentum autocorrelation function and thus provides a reasonable prior. We note that the MEAC+classical can still be extended to general autocorrelation functions as well, although one might have to adjust the prior spectrum [i.e., times the ratio C AA quantum (t=0) / C AA classical (t=0)] to obtain the exact value of the correlation function at zero time (t=0). Among all versions of quantum mechanics correlation functions, the Kubo-transformed correlation function is the one which most naturally corresponds to the classical correlation function, so it is reasonable that it provides the best choice to use in Eqs. for the MEAC+classical method.
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