Quantum dynamics and non-equilibrium physics

Geometry offers a different perspective on quantum states and their evolution. We use this perspective to study the information and structure carried by complex quantum systems.

In geometric quantum mechanics, pure states are points of the complex projective space $\mathbb{C}P^{D-1}$, while a geometric quantum state is a probability distribution on that space. This brings tools from differential geometry and dynamical systems into the study of quantum physics.

How do information, correlations, and entropy evolve in interacting quantum systems? We investigate the dynamics of complex quantum systems, including how they approach equilibrium and when they retain memory of their initial conditions.

Research in this direction connects quantum information transport, many-body localization, and the information-processing resources embedded in physical dynamics.

Ensembles connect microscopic quantum descriptions to statistical predictions. We study how to characterize ensembles, identify the information needed to describe them, and understand the role of constraints in equilibrium and non-equilibrium physics.

This direction brings together geometric entropy, quantum thermodynamics, and observable-based descriptions of statistical mechanics. It connects directly to our research on the quantum foundations of thermodynamics.