Summer research@Bucknell University - the simulation of waves
The localization of classical waves in linear and nonlinear disordered media has been extensively studied in the context of the nonlinear Schr¨odinger equation. We propose to extend these works and study the spreading and transport of waves described by the massive Klein-Gordon equation with a random position dependent mass and various nonlinear terms. Our studies are largely numerical, and the methods are susceptible to instabilities that lead to unphysical results. We referred to the existing literature to check if our numerical solution matches theirs, in order to further simulate the wave spreading in random position dependent potentials. We anticipate localization and plan to study the conserved quantities in such a regime, which can give us insights on how to understand the pattern of quantum waves spreading in position dependent potentials. In this poster we describe some numerical techniques that seem appropriate for the task, and discuss their stability in the linear case. In particular, we extend the von Neumann stability analysis for the Crank-Nicolson method to the above case. We plan to explore other numerical method that can be suitable for our purpose to be able to describe the pattern of localization.
- Susquehanna Valley Undergraduate Research Symposium
- American Physical Society