The Anderson Hamiltonian

The Anderson Hamiltonian is a mathematical model used in physics to understand how electrons move in a material with impurities or disorder. It describes how electrons hop between atomic sites while experiencing random variations in their energy levels due to the irregular environment. This randomness can cause electrons to become localized, trapping them and stopping conduction, which helps explain phenomena like electrical insulators versus conductors. Essentially, the model captures how disorder affects electronic behavior in materials, providing insights into metal-insulator transitions and the role of impurities in solid-state systems.