Statistical and Mathematical Physics

The PhyStatMath group explores a broad range of problems in physics and at the interface with other disciplines. This includes soft and condensed matter physics, biophysics, fluid physics, random processes and their applications, quantum information, strongly correlated quantum systems, nanoscience, exact statistical physics, astrophysics, social physics, behavioral biology, and robotics.

Across this diversity of topics, a common thread is the use of advanced analytical, mathematical, and numerical methods to investigate complex systems made of many interacting constituents, often driven far from equilibrium.


Research Topics

  • Biophysics and soft matter physics: biological and physical active matter, biophysics of the cell, protein diffusion, biological motors, ionic transport, nanotubes and nanopores, polymers and DNA physics, membranes, and vesicles.
  • Social physics: game theory and competition, collective motion and collective decision-making processes in animal and human groups, social psychology, robotics, virtual reality, machine learning.
  • Physics of long-range interacting systems: self-gravitating gases, two-dimensional turbulence and stratified fluids, kinetic theories, non-Boltzmann quasi-equilibrium states, applications in astrophysics and cosmology.
  • Probability theory and stochastic processes and their applications: reaction-diffusion models, dynamic interfaces, persistence, chemotaxis, diffusion in the presence of disorder or absorbers, random matrices and tensors, free probability, optimization problems.
  • Strongly out-of-equilibrium systems: dynamic phase transitions, phase separation, coarsening, and glassy dynamics.
  • Quantum information: quantum entanglement (separability problem, multipartite systems, dynamics…), quantum measurements and incompatibility, Bell nonlocality, tensor norms, random quantum states and channels, random tensor networks, quantum marginal problems. 
  • Strongly correlated quantum systems: interacting quantum gases and their mixtures, topological states of matter, fractional statistics, quantum phase transitions.

Methods

  • In addition to numerous collaborations with experimental groups, several members of the group are involved in the design and even the execution of experiments. Alongside analyzing experimental data, these physicists develop methods to extract parameters or signatures of phenomena linked to theoretical models from experimental measurements.
  • Stochastic processes and stochastic equations of motion are common tools used by all members of the group, whether applied to mathematical models studied analytically or simulated numerically.
  • In various contexts, the team exploits a wide range of advanced mathematical tools from statistical physics for systems composed of large numbers of interacting particles: field theory (including bosonization and conformal field theory), kinetic theories, Bethe ansatz, random matrices and random tensor techniques, free probability, tensor theory, tensor networks, and operator-algebraic tools.
  • From a numerical perspective, team members use various methods derived from statistical physics, such as Monte Carlo simulations, molecular dynamics, fluid equations coupled with matter, as well as diverse optimization techniques and machine learning.

Team members

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