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##### Friction coefficient within the AR model

The friction coefficient is defined as the integral over the memory function. In the discrete case we write

| (4.96)

As shown in [57], the AR model allows us to express as

| (4.97)

where the coefficients are given by eq. (4.76), and the roots must fulfill the stability criterion (4.77). Inserting (4.97) into (4.81) yields , the z-transform of the discrete memory function within the AR model,

| (4.98)

Using (4.98) we obtain thus within the AR model

| (4.99)

This shows that can be obtained from the zeros of the characteristic polynomial , defined in (4.74).

In the framework of the autoregressive model, nMOLDYN allows one to calculate the VACF, the VACF memory function, the DOS, the MSD, and the AR coefficients of the velocity trajectory, averaged over all selected atoms and three Cartesian coordinates.

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