A model of tunneling point defect in a quantum crystal at finite temperature

Abstract

With a very simple model, using the Kubo method, we treat the effect of phonons on the tunneling of a point defect in a quantum crystal and find the results of Kagan and Klinger. We concentrate on the case where spins play no part and consider in some detail the case of a vacancy in solid 4He. Some of our conclusions apply also to the decrease of the diffusion coefficient with temperature recently observed for 3He impurities in solid 4He.