The aim of the school is to introduce beginning PhD students to the physics of out-of equilibrium dynamics and thermalisation occuring in quantum many-body systems. The focus will be on learning numerical tools and methods to address and resolve model problems occuring in the context of condensed matter systems and ultracold atomic gases.

The level of precision and control reached in cold-atom experiments as well as advances in spectroscopic measurements on condensed matter materials require more and more theoretical and computational tools able to describe quantitatively time-dependent phenomena in quantum many-body systems. Computing the real-time (unitary) dynamics of a general, interacting quantum many-body system is an extremely challenging task, with broad applications. In this school we will focus on well-chosen model-like systems realized within ultracold atomic gases or condensed matter spin systems. In particular we want to address general topics related to thermalization or its absence (many-body localization), relaxation dynamics after quantum quenches and time-dependent driving in Floquet systems. Further, the dynamics of these quantum many-body models is intrinsically connected to questions in the field of quantum computing.

On the methodological side, the school aims to introduce computational tools which bridge the gap between (under)graduate numerical courses to more advanced techniques needed to address dynamical phenomena in closed open quantum systems. In the main courses we plan to provide detailed descriptions of the variety of numerical methods used in this context (in a broad sense), and, importantly, also practical examples based on small python programs. More specific and specialized algorithms and practical applications will be treated with seminars. A non-exhaustive list of computational methods include matrix-product states, exact diagonalization, Monte Carlo methods, and machine learning approaches.

Due to the recent changes in the French policies to limit the Covid pandemics we have to cancel the possibility of "on-site" attendance. The School will take place entirely online.

• Fabien Alet
  (LPT, Toulouse)
• Denis Basko
  (LPMMC, Grenoble)
• Nicolas Laflorencie
  (LPT, Toulouse)
• Alberto Rosso
  (LPTMS, Orsay)
  
• Markus Holzmann
  (LPMMC & ILL, Grenoble)

• Mari-Carmen Banuls
• Giuseppe Carleo
  
• Anushya Chandran
  
• Michel Ferrero
• Serge Florens
  
• David J. Luitz
• Markus Heyl
• Katharina Hyatt
• Adam Nahum
• Tommaso Roscilde
• Lea Santos
• Marco Schirò
• Cécile Repellin
• Guillaume Roux
  
• Xavier Waintal

• Murielle Gardette
  
• Anny Glomot