Dyson's Brownian Motion

Dyson's Brownian Motion describes how the energy levels of complex quantum systems, such as heavy atoms or heavy nuclei, fluctuate randomly over time. Imagine particles or numbers that evolve smoothly yet unpredictably, influenced by surrounding factors, akin to pollen grains drifting in water. This model captures the statistical behavior of these energy levels, revealing patterns and correlations, and is fundamental in understanding phenomena in quantum physics and mathematical fields like random matrix theory. Essentially, it models the intricate, random dance of energy states in complex quantum systems.