A single mathematical model can describe how atoms arrange in a semiconductor, how a polymer folds, and how a flock of birds moves—and theorists at Cambridge are building those models. This programme grant supports fundamental theoretical physics that sits between pure mathematics and experimental discovery. The researchers create mathematical frameworks to explain why matter behaves as it does, from the quantum behaviour of electrons in a crystal to the self-organisation of soft materials. Without such theory, experimental results remain isolated observations rather than generalisable knowledge. The work has no single immediate application. Instead, it builds the conceptual and computational toolkit that other scientists use to design new materials, improve semiconductor devices, or understand biological assembly processes like DNA folding. Past fundamental theory in condensed matter gave us transistors, lasers, and magnetic resonance imaging. This research could similarly underpin future technologies—ultracold atom sensors, more efficient electronics, or new ways to manufacture complex molecules—but the path from equation to device typically takes decades.
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As theoreticians, we construct models of physical and chemical processes that are generally inspired by experimental discoveries, we generalise these models and their solutions to make predictions for new experiments, and we transfer the concepts and theoretical tools which emerge from the solution of these models to other areas of research, in a concerted interdisciplinary effort. In short, the role of theory is to understand known phenomena observed in the laboratory or in everyday life, and to predict new physical processes and phenomena.Our theoretical research is both about making calculations, to quantitatively understand and predict the behaviour of matter, but also about making models to illuminate the landscape of emergent behaviour in physics, chemistry, material science, and biology. The role of theory includes both fundamental knowledge creation and practical applications of modelling for new and existing technology. The applications of our activity are as various as ultracold atoms, semiconductor devices and DNA assembly.Starting from first principles on the microscopic level (as embodied in the Schrdinger equation) electronic, mechanical and structural properties of molecules and materials can now be calculated with a remarkable degree of accuracy. We work on developing and refining new computational tools and applying them to a broad spectrum of fundamental and applied problems in physics, chemistry, materials science and biology.Solids and fluids often show unusual collective behaviour resulting from cooperative quantum or classical phenomena. For such phenomena a more model-based approach is often appropriate, and we are using such methods to attack problems in magnetism, superfluidity, nonlinear optics, mesoscopic systems, complex fluids and solids, andbio-polymers. Collective behaviour comes even more to the fore in systems on a larger scale. As examples, we work on self-organising structures in soft condensed matter systems, non-linear dynamics of interacting systems, and models of biophysical processes, all of which bridge the gap between molecular and mesoscopic scales.
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