"Discovering hydrodynamic equations of many-body quantum systems", arXiv:2111.02385

Framework for data-driven discovery of PDEs in many-body quantum systems from real-time dynamics

Summary

In this project we develop a new machine-learning framework for automated discovery of effective equations describing dynamics of many-body quantum systems, thus bypassing complicated analytical derivations. Using integrable models, where direct comparisons can be made, we reproduce previously known hydrodynamic equations, strikingly discover novel equations.

List of examples provided in the Jupyter notebooks

• Single magnon dynamics in 1D XXZ model
• Domain wall evolution in XXZ model (zero temperature and infinite temperature limits)
• Free fermion dynamics in a tight-binding J1-J2 model
• Interacting fermions dynamics in a spinless Fermi-Hubbard model
• Experimental data analysis: expansion of interacting boson gas on atom chip

Citation

@article{kharkov2021discovering,
  title={Discovering hydrodynamic equations of many-body quantum systems},
  author={Kharkov, Yaroslav and Shtanko, Oles and Seif, Alireza and Bienias, Przemyslaw and Van Regemortel, Mathias and Hafezi, Mohammad and Gorshkov, Alexey V},
  journal={arXiv preprint arXiv:2111.02385},
  year={2021}
}