Quantum coherence of a narrow band interacting with phonons and static disorder

This work deals with the quantum dynamics of a narrow band particle interacting with phonons and static disorder. The present theory is exact in the limit of small band width compared with the Debye energy, and covers various regimes in the parameter space of temperature and disorder strength. Therefore, the theory provides a unified framework for studying when and how the particle motion changes from coherent band like behavior to incoherent hopping, as the temperature and/or disorder strength are increased. The theory also includes the double well problem as a special case, where rather complete description of the particle motion is obtained.