Collective behavior of tunneling systems in amorphous solids

An open question in condensed matter physics is the origin of the universal properties of amorphous insulators, glasses in particular, at low temperatures. What is the reason for the amazingly broad applicability of the two-level system (TLS) model of low energy excitations in disordered insulators? Interactions between tunneling defects, deliberately omitted in the original model, may be the key to understanding the properties of these materials. This thesis contains several experiments which examine the importance of TLS-TLS interactions. After introducing the theory of the dielectric and acoustic response of these materials, nonequilibrium measurements are described. I compare the acoustic and dielectric responses, and their differences are interpreted as evidence for the growth of collective excitations of interacting TLS as the temperature is lowered. New and surprising thermal conductivity measurements down to 10 mK are described and presented, with an emphasis on the effects of TLS interactions on thermal transport. Finally, the equilibrium dielectric responses of three "fragile" glass-forming materials are presented.