Systèmes complexes

The aim of this lecture is to provide a description of quantum transport in disordered systems, with an emphasis on important phenomena like weak localization, Anderson localization and the Anderson metal-insulator transition. During the lecture, a number of important theoretical tools needed to describe quantum particle scattering in the presence of spatial disorder will be introduced in a pedagogical fashion, such as the Green's function technique, diagrammatic approaches to weak localization and transfer matrices. The lectures will be also illustrated by experimental examples and tutorials, especially taken from the physics of quantum gases and  condensed matter.

The lectures offer a statistical-physics perspective on active matter, which encompasses systems whose fundamental constituents dissipate energy to exert forces on the environment. This out-of-equilibrium microscopic drive endows active systems with properties unmatched in passive ones. From molecular motors to bacteria and animals, active agents are found at all scales in nature. Over the past twenty years, physicists and chemists have also engineered synthetic active systems in the lab, by motorizing particles whose sizes range from nanometers to centimeters, hence paving the way towards the engineering of active materials.

The lectures will rely on the modern tools of statistical mechanics, from stochastic calculus to field theoretical methods, using both theoretical models and experimental systems to illustrate the rich physics of active matter.

Computational physics plays a central role in all fields of physics, from classical statistical physics, soft matter problems, and hard-condensed matter. Our goal is to cover the basic concepts underlying computer simulations in classical and quantum problems, and connect these ideas to relevant and contemporary research topics in various fields of physics. In the TD’s you will also learn how to set, perform and analyse the results of simple computer simulations by yourself, covering a wide range of topics. We will use Python, but no previous knowledge of this programming language is needed.

    Can the whole not merely be the sum of its parts? How do collective patterns appear?
    Could three molecules of water form ice?
    Could higher-level abilities be created from interacting AI agents?

The notion of complexity pertains to systems in which somewhat unexpected properties emerge from the interplay of a sufficiently large number of  entities — be they particles, living cells, artificial neurons, organisms, people, abstract agents... or even a mixture of some (or all!) of these.

Statistical physics has been the first branch of science to try and model in a mathematical manner such systems, focusing especially on the subtle and often elusive passage from the micro/individual level to the macro/collective level. This lecture course explores further how the mindset of statistical physics can provide fertile ground for the analysis and modelling of complexity, across disciplinary boundaries.