18.337 Project: A Random Walk with Julia

The characteristic vibrational modes of a physical system are determined by the potential energy term of the system’s Hamiltonian. These vibrations are of interest because of their properties govern thermal transport in semiconductors,The second order derivatives of the potential energy with respect to displacements about the equilibrium position of the atoms, colloquially referred to as the second order force constants, is a positive definite blockdiagonal Hessian matrix. We start with the simple one-dimensional massspring configuration, as shown in Fig. 1. Here, un is the displacement from equilibrium of the nth atom with mass m and Un is the displacement from equilibrium of the nth of atom with mass M . The equations of motion of a linear diatomic chain considering only nearest neighbour interactions (K1