The objective of this course is to cover the background required to understand one major system in future quantumbased technologies in the solid state, namely localized spins of atoms embedded in a solid state matrix.

The main goal of this course is to provide an advanced view of the optical response of quantum materials. 

The goal of this course is to introduce the main methods in electronic structure theory, which is at the heart of our present capability of understanding, predicting, and engineering materials properties based on accurate in-silico solutions of the many-body Schrödinger equation for electrons and their coupling with the lattice/structural degrees of freedom. 

Recent years have seen enormous experimental progress in preparing, controlling and probing quantum systems in various regimes far from thermal equilibrium. Examples include systems as ultra-cold atomic quantum gases under time-dependent perturbations, driven non-linear cavity QED systems or strongly correlated electrons in solid-state materials under ultra-fast optical excitations.

Students performing a library-based project are expected to study a series of original research articles around a common subject, under the supervision of a senior researcher.

La théorie de la Relativité Générale est une modélisation des liens entre matière et gravitation à travers des équations reliant des objets géométriques.

These lectures present the study of instabilities or bifurcations of nonlinear systems and the resulting dynamic behaviors.

Superfluidity (like its cousin, superconductivity) is a particularly striking and concrete manifestation of the wavelike nature of matter. In electromagnetism, it is often fruitful to use Maxwell’s equations, forgetting about the existence of photons. Similarly, we will describe matter by a classical (complex-valued) field, forgetting about the existence of particles. This unconventional approach greatly helps to understand and derive the fundamental concepts and relations of superfluidity, under very general conditions (for any temperature below the transition temperature, including in 2 dimensions —where there is no condensate— and in presence of disorder —where there is no Galilean invariance). Superfluidity appears to be the natural state of the classical field, which can only be destroyed by topological defects (vortices). More formally, superfluidity is associated to a topological order, characterized by an emergent constant of motion. This will allow us to derive key equations of two-fluid hydrodynamics, which will enable us to explain key phenoma such as the fountain effect, the Josephson effect, or supertransport of heat.