The ERC Ph.D. project scrutinizes a fundamental question at the heart of the condensed matter, statistical and nonlinear physics: When far from equilibrium, in the presence of fluctuations, and faced with multiple steady states with small energy differences, how does a system evolve? This question underlies innumerable phenomena happening in complex systems every day, which we cannot predict, mimic, or control.
Dynamic adaptive systems are ubiquitous in nature, but they are too complex for a first-principles approach. Experimental systems created in the lab suffer from the same problem. Our uniquely simple colloidal system operates far from equilibrium under highly nonlinear and strongly stochastic conditions, where potential energy surfaces change over time and due to varying external parameters. Therefore, self-assembled aggregates of mesoscale particles can form various patterns ranging from the five basic Bravais lattices (in 2D) to more complex lattices resulting from their superpositions, such as quasicrystals, clathrates, Moiré patterns, honeycomb, and kagome lattices, and more. These crystals exhibit dynamic adaptive behaviour similar to those commonly associated with living organisms.
In the ERC Ph.D. project, we use these dissipative colloidal crystals as a model system to address this fundamental question. Our goal is to create a phase map, similar to a phase diagram of thermodynamics, but where each phase (here, crystal pattern) is dynamic and of finite occupation probability. We will use a convenient tool, fitness landscapes, which originates from evolutionary biology, to describe the stability of each phase in various conditions. We will further ask if this control can be extendable down to the few-nm scale, where fluctuations are much more substantial, and if and how these findings change when using nonidentical, in size or shape, active or passive particles?
