2009/06/03 by Mathieu Lewin, Robert Seiringer · 47 citations
Mathematics · Physics and Astronomy · #Bose gas #Bose–Einstein condensate #Boson #Cold Atom Physics and Bose-Einstein Condensates #Electron #Ground state #Hamiltonian (control theory) #Landau quantization #Mathematical physics #Mathematics #Physics #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Scattering #Wave function #cond-mat.quant-gas #math-ph #math.MP
paper · pdf · doi:10.1007/s10955-009-9833-y
published in Journal of Statistical Physics 137(5-6), 1040-1062 (Springer Science+Business Media) · AMSLaTeX, 23 pages
arxiv created 2009/06/03 · openalex publication_date 2009/10/06 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.