Abstract
Many unsolved riddles in the glassy and liquid state of matter seem to be connected with the low-frequency excitations in the millielectron volt range. In glasses, an interpretation of neutron scattering and specific heat data in terms of the soft-potential model (an extension of the tunnelling model) indicates a relatively high number of atoms partaking in a soft vibrational or tunnelling mode. The estimated number of about 100 participating atoms has been confirmed recently by numerical work in a glass of soft spheres. In the undercooled liquid, the number of soft modes seems to increase with increasing temperature. An explanation for their localization is attempted in terms of the balance between their vibrational entropy and the energy needed for their destabilization.