My research lies at the interface between many body quantum physics, quantum information theory and statistical physics.
In recent years, the progress in quantum engineering has provided new tools for simulating and studying the quantum dynamics of truly isolated quantum systems. These systems, made of trapped ions or cold atoms in optical lattices, can be prepared in a global pure state and their level of isolation from uncontrolled degrees of freedom is such that they can evolve unitarily according to the Schrödinger equation. Surprisingly, despite these systems are at all times in a pure quantum state, they can display some signatures of thermalization. More strikingly, these systems can sometimes display local equilibrium states in strong disagreement with the standard statistical physics predictions. These experimental facts are clearly questioning what kind of statistical description is relevant for isolated many body quantum systems.
The aim of my current project is to investigate theoretically and numerically new methods for characterizing the out of equilibrium dynamics, the stationary properties and the quantum information propagation in large interacting quantum systems. In other words, we are interested generally in the many body quantum problem. The method we propose involves the introduction of a controlled amount of randomness in the modeling of the physical system considered, in particular in the interaction between its subparts. We think this framework could provide statistical solutions to the many body problem.