Preliminary test of time-convolutionless mode-coupling theory based on the Percus-Yevick static structure factor for hard spheres

In order to investigate how the time-convolutionless mode-coupling theory (TMCT) recently proposed by Tokuyama can improve the critical point predicted by the ideal mode-coupling theory (MCT), the TMCT equations are numerically solved based on the Percus-Yevick static structure factor for hard spheres as a preliminary test. Then, the full numerical solutions are compared with those of MCT for different physical quantities, such as intermediate scattering functions and diffusion coefficients. Thus, the ergodic to nonergodic transition predicted by MCT is also found at the critical volume fraction $\phi_c$ which is higher than that of MCT. Here $\phi_c$ is given by $\phi_c\simeq 0.5817$ at $q_c\sigma_d=40$ and 0.5856 at $q_c\sigma_d=20$ for TMCT, while $\phi_c\simeq 0.5159$ at $q_c\sigma_d=40$ and 0.5214 at $q_c\sigma_d=20$ for MCT, where $q_c$ is a cutoff of wave vector and $\sigma_d$ a particle diameter. The same two-step relaxation process as that predicted by MCT is also discussed.