Electric current autocorrelation function

Figure 18 Normalized electric current autocorrelation function of [C2mim][Cl] at 486 K and 1 bat (bold solid line) total velocity autocottelation function (dashed line) and diffetence between them (gray). The inset shows the running integral of the electtical conductivity (gtay line), togethet with the best-fit exponential decay function (black line). (Ftom Ref. 107 and used with petmission.)...

The electrical conductivity, a, is calculated as the time integral of the electrical current autocorrelation function ... 

Before leaving the topic of Green-Kubo integrals for transport properties, we mention briefly the characteristics of the electric current correlation functions that are used to compute the electrical conductivity. Figure 18 shows the electric current and velocity autocorrelation functions for [C2mim][Cl] at 486 K and 1 bar. The current fluctuations decay rapidly and appear to vanish... 

Examples of linear response functions (susceptibilities) include the frequency dependent electrical conductivity (the Fourier transform of an equilibrium current autocorrelation function), dielectric susceptibility, which is the transform of a dipole moment autocorrelation function, along with stress, heat flux, and an assortment of velocity correlation functions. 

Since j-c-v, the electrical current density autocorrelation function and the velocity autocorrelation function are proportional to each other. The latter function, however, can be expressed with the help of the time derivative of the decaying pro-... 

Using linear response theory and noting (according to the results at the end of Section 5.1.3) that the (complex) electrical conductivity a is the Fourier transform of the current density autocorrelation function, we obtain from Eqn. (5.75) (see the equivalent Eqn. (5.21))... 

The molecular dynamics calculation of electrical conductivity in ionic fluids has been approached in several different ways. The autocorrelation function of the current may be related to the conductivity by... 

There are two other means of obtaining the trical conductivity from the same computation, amount of heat extracted from the system at each was recorded and divided by the square of the rent. The resulting quantity is also the conductivity. Values obtained in this way are also shown in Fig.l (+ s). Finally the power spectrum of the electrical current in a field free system was computed and the autocorrelation function derived therefrom used to obtain the electrical conductivity via the well-known relationship (U ). The value so obtained is entered on Fig.l as an open circle. All of these methods are, in principle, equivalent. The highest accuracy is attached to the direct measurement of the mean current. 

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