Combined mean-field and semiclassical limits of large fermionic systems

@article{Chen2019CombinedMA,
title={Combined mean-field and semiclassical limits of large fermionic systems},
author={L. Chen and Jinyeop Lee and M. Liew},
journal={arXiv: Mathematical Physics},
year={2019}
}

We study time dependent Schr\"odinger equation for large spinless fermions with the semiclassical scale $\hbar = N^{-1/3}$ in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schr\"odinger equation into a BBGKY type of hierarchy for the $k$ particle Husimi measures. Further estimates are derived to obtain the weak compactness of the Husimi measures, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show… Expand