Exact results for collective behaviour of trapped Fermions have remained elusive. Apart from mean-field approaches (Local Density/Thomas-Fermi approximation), there has hardly been any progress on studying collective phenomena. I will give a brief review of some exact results in low dimensions. I will then discuss our recent results  for collective description of noninteracting fermions in a 2D harmonic trap rotating with a constant frequency and in the presence of an additional repulsive central potential. I will show that in the large-N limit, the bulk density has a rich and nontrivial profile with a hole at the center of the trap and surrounded by a multilayered “wedding cake” structure. I will discuss a rich phase diagram that emerges in this system. I will then discuss connections to orthogonal polynomials, unitary evolution of certain quantum spin chains and Random Matrix Theory.
 M. Kulkarni, S. N. Majumdar, G. Schehr, Phys. Rev. A 103, 033321 (2021)
Zoom link: https://zoom.us/j/98292249357?pwd=WW5DK2RoU1B2UXpwMFhIUmhpaiszdz09
Meeting ID: 982 9224 9357