# Math physicist first Slovenian to win two ERC advanced grants

Mathematical physicist Tomaž Prosen, a professor at the Faculty of Mathematics and Physics, University of Ljubljana, has won his second European Research Council (ERC) advanced grant for research in mathematical statistical physics.

In the project Quantum Ergodicity: Stability and Transitions (QUEST) Prosen will research the robustness of quantum chaos and quantum ergodicity for outside disruptions. As Prosen said, this is basic research in the field of mathematical statistical physics.

Ergodicity, which is the idea that a point of a moving system will eventually visit all the parts of the space that the system moves in, is one of the key characteristics of many-body systems (microscopic systems made of many interacting particles), but it is incredibly difficult to prove it mathematically, said Prosen.

His research team was able to identify one such solvable paradigm, called dual unitary quantum circuit.

In the last two to three years the dual unitary quantum circuits has become a hot topic of research since the circuits offer an ideal platform to test quantum computers, the faculty said.

As this is a special class of dynamic systems, a key question is how robust the analytical mechanisms of ergodicity are when faced with outside disruptions that destroy the structure and the ideal solvability of the system.

The main hypothesis of the project is that the dual unitary circuits have to be robust, said Prosen, adding that they are intuitively considering analogies from mathematics and chaos theory.

If the hypothesis can be proven at least partially, there are many interesting applications, such as the theory of condensed matter, quantum informatics, quantum field theory and quantum gravitational theory.

Prosen will receive €2.17 million in ERC funding for the project. His first priority will be to assemble a research team.

This is the 11th ERC project for the Faculty of Mathematics and Physics and the second for Prosen, who previously led the project called Open Many-body Non-Equilibrium Systems.

The ERC advanced grant is one of the most prestigious and competitive EU research grants, awarded to established, leading researchers with a track record of important research achievements in the past decade.