Relaxation of Hamiltonian dynamics in intermediate timescales and slow dynamics of glass-forming liquids

We examine to what extent the characteristic slow dynamics of glass-forming liquids can be reproduced by a single-particle model without randomness. Our results show that even a single-particle Lorentz gas without explicit randomness reproduces the behavior of several key observables such as mean-square displacement, non-Gaussian parameter, and dynamical susceptibility in close agreement with those of glass-forming liquids. Notably, α relaxation, characterized by a stretched exponential decay in the self-intermediate scattering function, emerges in the 3D Lorentz gas with a face-centered-cubic (fcc) lattice. The Vogel-Fulcher law is also observed in the single-particle Lorentz gas; however, the full range of the Vogel-Fulcher law is reproduced only when the dimensionality of the model is increased, indicating that the Vogel-Fulcher law originates from features intrinsic to higher-dimensional systems. Finally, we discuss the implications of intermediate timescales and finite-lifetime structures in light of recent advances in dynamical systems theory.