Low-energy collective excitations in quenched disordered solids, the motion of vacancies in quantum crystals, and transport in highly polarized Fermi liquids will be studied. NMR and thermal transport measurements will be used to study low temperature relaxation in orientational glass states of N2/Alkali metal solid mixtures and NaCN/KCN mixed crystals. The existence of universality classes for the growth kinetics of correlated clusters in quenched disordered systems will be tested. Quantum tunneling of vacancies in isotopic helium solid solutions close to the melting curve will be studied with pulsed NMR. The effects of the onset of degeneracy on spin diffusion and transport properties of small, highly polarized helium-three droplets phase separated from solid solutions will be studied.