Thomas-Fermi profile of a fast rotating Bose-Einstein condensate

Abstract

We study the minimizers of a magnetic 2D non-linear Schrödinger energy functional in a quadratic trapping potential, describing a rotating Bose-Einstein condensate. We derive an effective Thomas-Fermi-like model in the rapidly rotating limit where the centrifugal force compensates the confinement, and available states are restricted to the lowest Landau level. The coupling constant of the effective Thomas-Fermi functional is linked to the emergence of vortex lattices (the Abrikosov problem). We define it via a low density expansion of the energy of the corresponding homogeneous gas in the thermodynamic limit.

The previous version, submitted in August 2022, had an unphysical restriction on the allowed scaling of physical parameters of the problem. We bypass this by a kind of bootstrap argument. We also correct a mistake in the proof of the density convergence in the LLL case

References in corpus (24)

• Vortex formation in a stirred Bose-Einstein condensate
• Rapidly Rotating Bose-Einstein Condensates in and near the Lowest Landau Level
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Bose-Einstein Condensates with Large Number of Vortices
• Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
• On the Dynamics of Large Particle Systems in the Mean Field Limit
• Vortex patterns in a fast rotating Bose-Einstein condensate
• Experimental studies of equilibrium vortex properties in a Bose-condensed gas
• Vortex lattices in the lowest Landau level for confined Bose-Einstein condensates
• Vortices in Spatially Inhomogeneous Superfluids
• Strongly correlated phases in rapidly rotating Bose gases
• Rotating superfluids in anharmonic traps: From vortex lattices to giant vortices
• Vortex distribution in the Lowest Landau Level
• On the Cubic Lowest Landau Level Equation
• Vortex Lattice Inhomogeneity in Spatially Inhomogeneous Superfluids
• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime
• Lowest Landau Level vortex structure of a Bose-Einstein condensate rotating in a harmonic plus quartic trap
• Local density approximation for the almost-bosonic anyon gas
• Vortex patterns in the almost-bosonic anyon gas
• Growth of Sobolev norms for coupled Lowest Landau Level equations
• The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps
• Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates
• Holomorphic quantum Hall states in higher Landau levels