Three-point susceptibilitiesχn(k;t)andχns(k;t): Mode-coupling approximation
Physical Review E
Recently, it was argued that a three-point susceptibility equal to the density derivative of the intermediate scattering function, χ_n(k;t) = d F(k;t)/d n, enters into an expression for the divergent part of an integrated four-point dynamic density correlation function of a colloidal suspension [Berthier et al., J. Chem. Phys. 126, 184503 (2007)]. We show that, within the mode-coupling theory, the equation of motion for χ_n(k;t) is essentially identical as the equation of motion for the q→ 0
... it of the three-point susceptibility χ_q(k;t) introduced by Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)]. We present a numerical solution of the equation of motion for χ_n(k;t). We also derive and numerically solve an equation of motion for the density derivative of the self-intermediate scattering function, χ_n^s(k;t) = d F^s(k;t)/d n. We contrast the wave vector dependence of χ_n(k;t) and χ_n^s(k;t).