Thanks to their high degree of control and tunability, ultracold atomic gases provide a rich platform for the study of quantum many-body effects. Ultracold gases of highly magnetic atoms exhibit unique interaction properties that lead to striking behaviors, both at the mean-field level and beyond [1]. A decade ago, a universal stabilization mechanism driven by quantum fluctuations was discovered in these gases. This mechanism prevents the systems from collapsing when the mean-field interactions become attractive, and instead allows exotic states of matter to arise, including ultradilute quantum droplets, crystallized quantum states, and especially the so-called supersolids [2]. In my colloquium, I will present the seminal observations of these states and how they emerged from the long-standing progress in the field. I will discuss the theoretical description of these systems via an effective mean-field theory, including the effect of quantum fluctuations via a higher-order effective interaction. I will outline our current understanding of the properties of these states and highlight open questions.

[1] L. Chomaz & al, Dipolar physics: a review of experiments with magnetic quantum gases, Reports on Progress in Physics 86, 026401 (2023).

[2] L. Chomaz, Quantum-stabilized states in magnetic dipolar quantum gases, arXiv preprint 2504.06221 (2025)

_____________________

Invited by Prof. Arnaud Triay

We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled system of stochastic Fredholm equations, which we solve in terms of operator resolvents. When the agents' interactions are modeled by a weighted graph, we formulate the corresponding non-Markovian continuum-agent game, where interactions are modeled by a graphon. We also derive the Nash equilibrium of the graphon game explicitly by first reducing the first-order conditions to an infinite-dimensional coupled system of stochastic Fredholm equations, then decoupling it using the spectral decomposition of the graphon operator, and finally solving it in terms of operator resolvents. Moreover, we show that the Nash equilibria of finite-player games on graphs converge to those of the graphon game as the number of agents increases. This holds both when a given graph sequence converges to the graphon in the cut norm and when the graph sequence is sampled from the graphon. We also bound the convergence rate, which depends on the cut norm in the former case and on the sampling method in the latter. Finally, we apply our results to various stochastic games with heterogeneous interactions, including systemic risk models with delays and stochastic network games. ______________________________

Invited by Prof. Alexander Kalinin