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

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 $k^{\mathrm{th}}$ layer, we find that the edge density profile exhibits $k$ kinks located at the zeroes of the $k^{\mathrm{th}}$ 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.

17 pages, 10 figures. Published version, with typos corrected

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Cited by in corpus (10)

• Full counting statistics for interacting trapped fermions
• Counting statistics for non-interacting fermions in a rotating trap
• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• Quantum statistics transmutation via magnetic flux attachment
• Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature
• Hole probability for noninteracting fermions in a $d$-dimensional trap
• Spatio-temporal fluctuations in the passive and active Riesz gas on the circle
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions
• Linear statistics at the microscopic scale for the 2D Coulomb gas