PHONON COUPLING IN TUNNELING SYSTEMS AT ZERO TEMPERATURE: AN INSTANTON APPROACH

I present a new method for dealing with phonon modes in path integrals. Using it and an instanton expansion, I have developed a detailed theory of the tunneling event in the presence of phonons. I have used an instanton expansion to compute tunnel splittings and decay times for the coupled system, and have compared the results in detail with traditional two-level models for point tunneling defects in solids. For electron tunneling with a weak phonon coupling, the two level models are found to be adequate. For atomic tunneling and strongly coupled electronic tunneling (i.e. where self-trapping is a component of the effective potential) the two level models can be used if at all only in a renormalized sense.; I also develop other physical approximations and compare them with the (asymptotically exact) instanton calculations. As noted above, the two level 'truncation approximation' is natural in dealing with tunneling of weakly coupled electrons. Atomic tunneling is demonstrably best described by an effective mass due to the coupled lattice motion. Strongly coupled electrons are treated using an approximation valid for self-trapped tunneling. In the same vein, I develop a renormalized truncation approximation, which explains the successes and failures of the use of two level systems to describe tunneling.; I apply these techniques to two physical systems. I do a detailed calculation of the isotope effect in KCl:Li('+) as an example of the effective mass approximation. I illustrate the nature of self-trapped tunneling by investigating the likelihood of tunneling of Anderson's negative U-centers in amorphous semiconductors.