Inelastic Scattering off a Nanomechanical Resonator

We study the dephasing rate of conduction electrons due to local vibrational modes. Bosonization allows us to evaluate the full T-matrix analytically. The inelastic scattering rate is strongly influenced by multiphonon excitations. For higher frequencies, it saturates to a finite, coupling dependent value. In the strong coupling limit, the phonon is almost completely softened, and the inelastic cross section reaches its maximal value. This represents a magnetic field insensitive contribution to the dephasing time in mesoscopic systems, in addition to magnetic impurities.