PhD defence: Fractional Dissipation, Magnetization Dynamics, and Long-Range Interactions in Fractals

In microscopic systems, particles constantly interact with their surroundings, losing energy to the environment as heat. This energy loss has two effects: random fluctuations (noise) and dissipation (friction). Remarkably, this friction knows about its history. We describe this memory using a mathematical tool called a fractional derivative. Depending on the type of memory, different physical behaviors can emerge.

We applied this idea, called fractional dissipation, to two key systems. First, we studied a model of a liquid and found that it could transition into a glass, a newly discovered “time glass” phase, and finally a marginal glass. This allowed us to describe four distinct states of matter within a single equation. We also showed that this equation can appear in a range of different environments.

Next, we studied tiny atomic magnets, known as spins, and discovered a new fractional equation describing how the magnetisation inside materials changes over time. We proposed an experiment using existing techniques to measure the type of memory present in such magnetic systems.

Finally, we explored magnetic systems with fractal shapes – complex, self-repeating patterns found in nature. These systems involve long-range interactions that are very difficult to compute. Folding up the system like origami, we developed a new method, named SIM-GRAPH. This reduces computation time from days to minutes, for example. It also allows for calculating larger systems on regular computers, and revealed that magnetisation often forms stable patterns with a whole number of spins pointing up.

PLEASE NOTE: If a candidate gives a layman's talk, the livestream will start fifteen minutes earlier.