# Frederic HEBERT - Universite de Nice Sophia Antipolis - Keywords: Superfluids, Solids, Photons

The complexity and diversity of behaviors observed in materials comes from the collective behavior of the simple objects (atoms, molecules) constituting materials. The tools of statistical physics allow to derive the macroscopic properties of said materials starting from a microscopic description of its constituents. In most cases, the emergent behavior pertains to simple categories: solid or liquid, insulator or conductor… But in some cases, complex behaviors such as superfluidity or superconductivity, where the wave like behavior of quantum objects subsist at a macroscopic scale, emerge. Such unusual behaviors are generally the result of the collective behavior of different kinds of particles submitted to strong correlations, or of the competition between different effects, such as the competition between the wave and particle nature of quantum objects.

To study these emergent phenomenas, we focus mostly on discrete toy models that are simpler to study and analyze, which allows a better qualitative understanding of the phenomenas. We simulate the behavior of the models by means of quantum Monte Carlo simulations. Beyond their usefulness as toy models, discrete systems are ubiquitous in nature, whether they are natural ones, such as solids, or synthetic ones, such as atoms in optical lattices or quantum electrodynamics circuits. We will present some examples of these complex behaviors, namely in mixtures of particles moving in an underlying lattice or in assemblies of coupled optical resonators (Rabi systems).