Three-point susceptibilities ${\chi }_n(k;t)$ and ${\chi }_n^s(k;t)$: mode-coupling approximation

Abstract

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 \textit{et al.}, J. Chem. Phys. \textbf{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 $\mathbf{q}\to 0$ limit of the three-point susceptibility ${\chi }_{\mathbf{q}}(\mathbf{k};t)$ introduced by Biroli \textit{et al.} [Phys. Rev. Lett. \textbf{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, ${\chi }_n^s(k;t)=d{F}^s(k;t)/dn$. We contrast the wave vector dependence of ${\chi }_n(k;t)$ and ${\chi }_n^s(k;t)$.

References in corpus (16)

• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
• Direct experimental evidence of a growing length scale accompanying the glass transition
• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture II: Intermediate Scattering Function and Dynamic Susceptibility
• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• On nonlinear susceptibility in supercooled liquids
• Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation
• Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass
• Lengthscale dependence of dynamic four-point susceptibilities in glass formers
• Dynamical Heterogeneity and Nonlinear Susceptibility in Short-Ranged Attractive Supercooled Liquids
• Self-consistent mode-coupling theory for the viscosity of rod-like polyelectrolyte solutions
• Divergent four-point dynamic density correlation function of a glassy colloidal suspension: a diagrammatic approach
• A theory for critically divergent fluctuations of dynamical events at non-ergodic transitions

Cited by in corpus (3)

• Diverging length scale of the inhomogeneous mode-coupling theory: a numerical investigation
• Dynamical Susceptibilities Near Ideal Glass Transitions
• Theory of the $\beta$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment