Solving puzzles in the quantum world

6 Oct 2023

Arnaud Triay is using mathematics to open up the world of quantum mechanics — in other words, he is applying mathematical methods to physics.

The Schrödinger equation is one of the fundamental equations of quantum mechanics. With a hypothetical supercomputer at your disposal, you could theoretically use this equation to describe almost all of the changes in the states of matter that occur in the universe. In practice, however, we lack this level of computing power, so physics relies on simpler mathematical models that may be less accurate but can be used to make predictions. And that’s where Arnaud Triay comes in, in his role as professor of analysis and mathematical physics at LMU since September 2022: “Starting from the core equation, I derive models and check whether they agree with the literature.” His tools of choice are pen and paper or a blackboard — and a whole lot of new ideas.

After studying mathematics at the École Normale Supérieure in Lyon, Triay earned his doctorate in Paris at Ceremade — Université Paris-Dauphine. “I have always loved both physics and the precision of mathematics,” he says. He first came to LMU to do his postdoc. “Munich is known as a quantum mechanics hotspot. The city has one of the highest concentrations of mathematical physics experts working in the quantum world.”

Professor Triay with glasses and in olive T-shirt with light gestures in front of a chalkboard with numerous mathematical calculations.

Professor Arnaud Triay conducts research at the interface of mathematics and physics.

© LC Productions

A playground for fundamental research

Arnaud Triay is one of the leading scientists in a Collaborative Research Center (CRC) funded by the German Research Foundation (DFG). In the CRC’s project, he is working on deriving special models in connection with so-called Bose–Einstein condensates. Put simply, the universe consists of two types of particles, bosons and fermions. We encounter fermions most often because they form the particles that make up the matter around us. They cannot be in the same place at the same time, which is why you can sit on a chair without falling through it. Bosons, on the other hand, do not have this property; they behave according to the rules of Bose–Einstein statistics, which allows several identical particles to occupy the same state. “For physicists, boson systems are a good playground for testing their theories,” Triay explains. “That gives them a way to continually improve the models.”

Even though he is a theoretical scientist through and through, Triay likes the idea that quantum mechanics has some very concrete applications today, for example in the development of new medications or in transistors. The field, he says, was originally developed by pure theoreticians who were less interested in the practical benefits but rather in expanding the frontiers of knowledge. But this still led to some very practical findings. “Quantum mechanics impacts our lives in many different ways without us even knowing,” says Triay.

What he particularly loves about his work is the fact that it is so varied. Many mathematicians are focused on a very specific subdomain. “The beauty of my field is that it is so broad and touches on many aspects of mathematics,” he says. “I really enjoy working at this interface.”

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