Energy transport and relaxation in one-dimensional Hamiltonian systems

Abstract

This thesis deals with phononic energy transport in one-dimensional systems, both quantum and classical. The chief application is to the behavior of thermal conductivity in nanowires and nanotubes. We are primarily concerned with the question of anomalous versus normal energy transport in these systems. Normal transport refers to uctuations that relax to equilibrium following the diffusion equation, for which well-defned transport coefficients exist. Anomalous diffusion, on the other hand, shows a more complicated mathematical behavior, and is characterized by diverging (or vanishing) transport coefficients. Energy diffusion in one-dimensional models is quite generally anomalous, though some specific conditions imposed on the model lead to normal transport. The central problem of this thesis is to understand and characterize anomalous transport properties of energy in one dimensional systems, and also to identify general criteria necessary for normal transport of energy