Chaotic properties of the soft-disk Lorentz gas

The traditional hard-disk Lorentz gas describes the chaotic motion of a classical point particle through an array of impenetrable disks. Soft-disk modifications of the two-dimensional Lorentz gas, where the scattering particle can move into the disk interiors, are considered here. Conditions on the soft-disk potentials and disk separations that guarantee chaotic motion are obtained.