{
"id": "2009.07251",
"version": "v1",
"published": "2020-09-15T17:37:20.000Z",
"updated": "2020-09-15T17:37:20.000Z",
"title": "Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap",
"authors": [
"Manas Kulkarni",
"Satya N. Majumdar",
"Gregory Schehr"
],
"comment": "Main text: 6 pages, 3 figures. Supplemental material: 15 pages, 7 figures",
"categories": [
"cond-mat.stat-mech",
"cond-mat.quant-gas",
"math-ph",
"math.MP"
],
"abstract": "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.",
"revisions": [
{
"version": "v1",
"updated": "2020-09-15T17:37:20.000Z"
}
],
"analyses": {
"keywords": [
"rotating two-dimensional trap",
"noninteracting fermions",
"multilayered density profile",
"quantum spin chains",
"rich phase diagram"
],
"note": {
"typesetting": "TeX",
"pages": 6,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}