  The boson peak in metallic glasses is modeled in terms of local structural
shear rearrangements. Using Eshelby's solution of the corresponding elasticity
theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can
calculate the saddle point energy of such a structural rearrangement. The
neighbourhood of the saddle point gives rise to soft resonant vibrational
modes. One can calculate their density, their kinetic energy, their fourth
order potential term and their coupling to longitudinal and transverse sound
waves.

Disordered Systems and Neural Networks