Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature

Abstract

We study the average density of $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\Omega$ and in the presence of an additional repulsive central potential $\gamma /r^2$. The average density at zero temperature was recently studied in Phys. Rev. A $\text{103}$, 033321 (2021) and an interesting multi-layered "wedding cake" structure with a "hole" at the center was found for the density in the large $N$ limit. In this paper, we study the average density at finite temperature. We demonstrate how this "wedding-cake" structure is modified at finite temperature. These large $N$ results warrant going much beyond the standard Local Density Approximation. We also generalize our results to a wide variety of trapping potentials and demonstrate the universality of the associated scaling functions both in the bulk and at the edges of the "wedding-cake".

arXiv comment18 pages, 7 figures, 1 table

References in corpus (50)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Rapidly Rotating Atomic Gases
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Rapidly Rotating Bose-Einstein Condensates in and near the Lowest Landau Level
• Single-atom imaging of fermions in a quantum-gas microscope
• A Quantum Gas Microscope for Fermionic Atoms
• Site-resolved Imaging of Fermionic Lithium-6 in an Optical Lattice
• Bose-Einstein Condensates with Large Number of Vortices
• Homogeneous Atomic Fermi Gases
• Trapped Fermi gases
• Two-Dimensional Homogeneous Fermi Gases
• Vortex patterns in a fast rotating Bose-Einstein condensate
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Universality in the full counting statistics of trapped fermions
• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Observation of shock waves in a strongly interacting Fermi gas
• Particle Number Fluctuations, Rényi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization
• Phase transitions and edge scaling of number variance in Gaussian random matrices
• Finite temperature free fermions and the Kardar-Parisi-Zhang equation at finite time
• Random matrices and entanglement entropy of trapped Fermi gases
• Exact short-time height distribution in 1D KPZ equation and edge fermions at high temperature
• Noninteracting fermions in a trap and random matrix theory
• Entanglement entropies in free fermion gases for arbitrary dimension
• Entanglement Entropy and Full Counting Statistics for $2d$-Rotating Trapped Fermions
• The entanglement entropy of 1D systems in continuous and homogenous space
• Multicritical edge statistics for the momenta of fermions in non-harmonic traps
• Entanglement and particle correlations of Fermi gases in harmonic traps
• Wigner function of noninteracting trapped fermions
• The equation of state of ultracold Bose and Fermi gases: a few examples
• Number statistics for $\beta$-ensembles of random matrices: applications to trapped fermions at zero temperature
• Universal ground state properties of free fermions in a $d$-dimensional trap
• Counting statistics for non-interacting fermions in a $d$-dimensional potential
• Rapidly Rotating Fermi Gases
• Free fermions at the edge of interacting systems
• Formation of a vortex lattice in a rotating BCS Fermi gas
• Full counting statistics for interacting trapped fermions
• Critical statistics for non-Hermitian matrices
• Ground state energy of noninteracting fermions with a random energy spectrum
• Current reversals in rapidly rotating ultra-cold Fermi gases
• Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature
• Periodic Airy process and equilibrium dynamics of edge fermions in a trap
• Statistics of fermions in a $d$-dimensional box near a hard wall
• Counting statistics for non-interacting fermions in a rotating trap
• Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap
• Kinetic energy of a trapped Fermi gas at finite temperature
• Fluctuations of observables for free fermions in a harmonic trap at finite temperature
• Free fermions and $\alpha$-determinantal processes
• Noninteracting trapped Fermions in double-well potentials: inverted parabola kernel

Cited by in corpus (4)

• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• Spatio-temporal fluctuations in the passive and active Riesz gas on the circle
• Linear statistics at the microscopic scale for the 2D Coulomb gas
• Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions