Classical Hamiltonian dynamics of a particle interacting with the vibrational modes of a one-dimensional medium

The polaron and more generally the basic problem of a particle interacting with the vibrational modes of the local medium are important to a large range of physical processes. The complex behavior and underlying properties of polaron dynamics has been the focus of much research for many years. Since the exact quantum mechanical dynamics of the interacting particle/many-oscillator system remains computationally complex due to the enormous size of the many-body Hilbert space, it is difficult to computationally test perturbative or semi-classical calculations of such fundamental transport quantities as the polaron diffusion constant. This thesis introduces a classical model which incorporates the essential features of a particle coupling to the surrounding vibrational modes. With this simple model it is possible to numerically evaluate the equations of motion allowing detailed examination of the dynamics. First, the nonlinear dynamics of a particle interacting with a single oscillator on a ring are explored, and after which the macroscopic transport properties are examined for a, particle moving on an infinite chain in which are periodically embedded oscillators to which the particle couples.