Heat Transport in Inhomogeneous Harmonic Chains

Sammanfattning: It is still to this day a challenge for theoretical physicists to derive Fourier’s law from microscopic models. Motivated by this, we study in this thesis the thermal conduction properties of harmonic chains. A semi-analytical method and simulation are used to find that on average the conduction through harmonic chains resembles Fourier like conduction when impurities of the form k_i=kw_i and 1/m_i=1/m'w_i are introduced, where k_i and m_i are the spring constants and masses of the chain and w_i are weights drawn from a random distribution. A few of these distributions are studied in detail, with similar results.Also the classical field theory limit of this model is studied. It is shown by analytical means that heat is transported diffusively in this model when impurities are introduced, whereas the transport is completely ballistic in the absence of impurities.