The Quantum Hall Effect

The quantum Hall effect is a well-known, but not yet fully explained, phenomenonin modern physics.  The quantum Hall effect arises when a strong magnetic field is applied to a low-temperature, two-dimensional electron... [ view full abstract ]

The quantum Hall effect is a well-known, but not yet fully explained, phenomenonin modern physics.  The quantum Hall effect arises when a strong magnetic field is applied to a low-temperature, two-dimensional electron system, causing the conductivity of the material to take on quantized values.  This seemingly bizarre result (and others) can be explained by describing the system mathematically in terms of its topological characteristic. In this project, I apply theoretical and computational methods of solution to described the quantum Hall effect and to other quantum systems.