Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 137, Issue 5-6, Pages 1040-1062Publisher
SPRINGER
DOI: 10.1007/s10955-009-9833-y
Keywords
Bose-Einstein condensation; Landau levels; Scattering length; Quantum Hall effect
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Funding
- ANR project ACCQuaRel of the French ministry
- U.S. National Science Foundation [PHY-0652356]
- Division Of Physics
- Direct For Mathematical & Physical Scien [0845292] Funding Source: National Science Foundation
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We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.
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