• DOI:10.1103/PhysRevA.103.033321
• Corpus ID: 221703079

Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap

@article{Kulkarni2020MultilayeredDP,
  title={Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap},
  author={Manas Kulkarni and Satya N. Majumdar and Gr{\'e}gory Schehr},
  journal={Physical Review A},
  year={2020}
}

• M. Kulkarni, S. N. Majumdar, G. Schehr
• Published 15 September 2020
• Physics
• Physical Review A

We compute exactly the average spatial density for $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\Omega$ in the presence of an additional repulsive central potential $\gamma/r^2$. We find 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 multi-layered "wedding cake" structure. The number of layers depends on $N$ and on the two parameters $\Omega$ and $\gamma$ leading to a rich phase diagram. Zooming in on the edge of the $k^{\rm th}$ layer, we find that the edge density profile exhibits $k$ kinks located at the zeroes of the $k^{\rm th}$ Hermite polynomial. Interestingly, in the large $k$ limit, we show that the edge density profile approaches a limiting form, which resembles the shape of a propagating front, found in the unitary evolution of certain quantum spin chains. We also study how a newly formed droplet grows in size on top of the last layer as one changes the parameters.