Quantum Dynamics of a Particle Interacting with Lattice Vibrations and Disorder Potentials

Abstract

Understanding the fundamental behavior of matter requires studying the quantum dynamics of a particle interacting with lattice vibrations and disorder potentials. In the first part of this dissertation, lattice vibrations are represented using the coherent state representation, resulting in a quasiclassical field that serves as a dynamic disorder potential for a particle. The dynamics of the particle within this potential are treated nonperturbatively to preserve coherence beyond single collision events. This approach is effective in capturing particle coherence effects and computing the density of states. Specifically, the low-energy tail of the spectral density is calculated and its relationship to static disorder potentials is established in the classical phonon limit. In the second part of the dissertation, it is shown that even in the absence of periodic structure in a static disorder potential, sharp Bragg diffraction of the wave is still observed. This phenomenon resembles a powder diffraction pattern but includes nontrivial partially resonant scattering that violates Fermi’s golden rule.