Phase diagram of gases with long-range interactions – GaLoPee
We are interested in describing the infinite volume behavior of systems of classical particles whose singular, long-range interactions create analytical and probabilistic challenges. From a mathematical perspective, these systems are large probabilistic objects which requires a wide range of tools in probability theory and functional analysis in order to support and enhance the physical intuition. A central question is to interpret their behavior in a statistical physics sense as the temperature varies. We also study them as a family, and examine the roles of dimension, singularity, and long-range. We aim at giving a unified phase portrait, in regard to properties such as rigidity, hyperuniformity or symmetry breaking. We shall combine tools from stochastic geometry with recent analytical developements, while forging new probabilistic techniques like transportation of point processes.
Monsieur Thomas Leblé (Mathématiques appliquées à Paris 5)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
MAP5 Mathématiques appliquées à Paris 5
Help of the ANR 182,571 euros
Beginning and duration of the scientific project: September 2021 - 36 Months