Light quantum particles in a metallic environment

The basic mechanism that limits the quantum behavior of light particles is fluctuations in the environment. We here develop a path-integral formalism that accounts for the influence of the environment on the quantum motion of such particles. As our prime example we discuss a particle that moves in a tight-binding band and interacts with an electron-gas environment. This situation has received experimental attention recently in the case of muon diffusion in metals and in the theoretical discussion of hydrogen on metal surfaces. It is shown that the adiabatic approximation, usually applied to such problems, does not work. This has basically two consequences. At low temperatures we find that the particle moves in Bloch states with a renormalized (more narrow) bandwidth. For higher temperatures (kBT>Wᵣₑₙ) the Bloch states acquire a lifetime that is shorter than {}/Wᵣₑₙ, which means a complete breakdown of the Bloch picture.