Anisotropic Interaction between Two-Level Systems

Using the model of interaction between two-level systems (TLS) and strain fields introduced in Phys. Rev. B 75, 064202 (2007), we calculate the TLS-TLS interaction. We particularize our calculations to amorphous materials and analyze the dependence of the interaction Hamiltonian on the orientations of the two TLSs and of the direction that connects them. Assuming isotropic distribution of the TLSs orientations, we then averaged the interaction over one of the TLSs orientations. The resulting interaction depends in a simple way on the angle between the orientation of the other TLS and the line that connects the two TLSs.