SIMBAD references

The equation κ_zz = dσ²/(2dt) describing the relation of the parallel diffusion coefficient κ_zz with the displacement variance σ² (hereafter DCDV) is a well-known formula. In this study, we find that DCDV is only applicable to two kinds of transport equations of the isotropic distribution function, one without cross-terms and the other without a convection term. Here, by employing the more general transport equation, i.e., the variable coefficient differential equation derived from the Fokker-Planck equation, a new equation of κ_zz as a function of σ² is obtained. We find that DCDV is the special case of the new equation. In addition, another equation of κ_zz as a function of σ² corresponding to the telegraph equation is also investigated preliminarily.