
Robert F. 2025 | BASIS Independent Silicon Valley
- Project Title: Analyzing the Quantum Hall Effect in Apollonian Gaskets
- BASIS Independent Advisor: Dr. Noble
- Internship Location: Remote - Imperial College London
- Onsite Mentor: Mr. Adam Almakroudi, Imperial College London - Faculty of Natural Sciences
In this project, we use both theoretical and computational methods to explore how electrons move in a fractal structure called an Apollonian gasket when a magnetic field is applied. The Schrödinger equation, which describes quantum mechanics at small scales, is used to understand how the electron behaves in this unique environment. Unlike normal materials, fractals have a repeating pattern at different scales, which leads to unusual energy levels and electron motion. By studying this system, we examine how the quantum Hall effect—an important phenomenon in condensed matter physics—appears in fractal materials. Using a mathematical model and numerical simulations, we analyze how the structure influences the electron’s energy states and conductivity. This research helps us understand quantum mechanics in new and complex geometries and could have applications in future electronic and quantum computing technologies.