Three-point susceptibilities chi(n) (k;t) and chi(n)s (k;t): mode-coupling approximation.
Recently, it was argued that a three-point susceptibility equal to the density derivative of the intermediate scattering function, chi{n}(k;t)=dF(k;t)dn , enters into an expression for the divergent part of an integrated four-point dynamic density correlation function of a colloidal suspension [Berthier, J. Chem. Phys. 126, 184503 (2007)]. We show that, within the mode-coupling theory, the equation of motion for chi{n}(k;t) is essentially identical as the equation of motion for the q-->0 limit of the three-point susceptibility chi{q}(k;t) introduced by Biroli [Phys. Rev. Lett. 97, 195701 (2006)]. We present a numerical solution of the equation of motion for chi{n}(k;t) . We also derive and numerically solve an equation of motion for the density derivative of the self-intermediate scattering function, chi_{n};{s}(k;t)=dF;{s}(k;t)dn . We contrast the wave vector dependence of chi{n}(k;t) and chi{n};{s}(k;t) .
Szamel
Grzegorz
G
Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA.
Flenner
Elijah
E