README.md

Study of Lattice Vibrations: Different Perturbations and Vibrational Modes

Abstract

In lattices where atoms are bound by the neighboring atoms and forces, the study of lattice vibrations can reveal information about the material’s properties. In this project, we will study the vibrational modes of a 1D lattice of $N$ atoms with the same mass m and nearest-neighbor interactions by employing a combination of numerical methods. By utilizing RK4 time stepping and FFT analysis, we explore the vibrational modes arising from various initial conditions and boundary constraints. Noteworthy observations include the manifestation of expected normal modes under specific perturbations and the implications of symmetric and random perturbations on mode development. Furthermore, the study underscores the method’s adaptability, paving the way for effortless exploration of diverse conditions and dimensions in lattice dynamics simulations.

Report available here. Slides available here.