2020/09/30 by Manas Kulkarni, Satya N. Majumdar, Grégory Schehr +1
Mathematics · Physics and Astronomy · #Center (category theory) #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Crystallography #Fermion #Hermite polynomials #Limit (mathematics) #Limiting #Mathematical physics #Omega #Phase (matter) #Phase diagram #Physics #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Strong Light-Matter Interactions #cond-mat.quant-gas #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1103/physreva.103.033321
published as Phys. Rev. A 103, 033321 (2021) · 17 pages, 10 figures. Published version, with typos corrected
openalex publication_date 2021/03/22 · arxiv created 2021/12/24 · arxiv updated 2021/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We compute exactly the average spatial density for N spinless noninteracting fermions in a 2d harmonic trap rotating with a constant frequency \mathrm\ensuremathΩ in the presence of an additional repulsive central potential \ensuremathγ/r2. 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 multilayered ``wedding cake'' structure. The number of layers depends on N and on the two parameters \mathrm\ensuremathΩ and \ensuremathγ leading to a rich phase diagram. Zooming in on the edge of the kth layer, we find that the edge density profile exhibits k kinks located at the zeros of the kth 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.