Journal of Statistical Physics

, Volume 154, Issue 1–2, pp 2–50 | Cite as

Quantum Hall Phases and Plasma Analogy in Rotating Trapped Bose Gases



A bosonic analogue of the fractional quantum Hall effect occurs in rapidly rotating trapped Bose gases: There is a transition from uncorrelated Hartree states to strongly correlated states such as the Laughlin wave function. This physics may be described by effective Hamiltonians with delta interactions acting on a bosonic N-body Bargmann space of analytic functions. In a previous paper (Rougerie et al. in Phys. Rev. A 87:023618, 2013) we studied the case of a quadratic plus quartic trapping potential and derived conditions on the parameters of the model for its ground state to be asymptotically strongly correlated. This relied essentially on energy upper bounds using quantum Hall trial states, incorporating the correlations of the Bose-Laughlin state in addition to a multiply quantized vortex pinned at the origin. In this paper we investigate in more details the density of these trial states, thereby substantiating further the physical picture described in (Rougerie et al. in Phys. Rev. A 87:023618, 2013), improving our energy estimates and allowing to consider more general trapping potentials. Our analysis is based on the interpretation of the densities of quantum Hall trial states as Gibbs measures of classical 2D Coulomb gases (plasma analogy). New estimates on the mean-field limit of such systems are presented.


Rotating Bose gases Bosonic Quantum Hall Effect 2D Coulomb gases 



NR thanks Xavier Blanc and Mathieu Lewin for helpful discussions during the early stages of this project. SS is supported by an EURYI award. Funding from the CNRS in the form of a PEPS-PTI project is also acknowledged. JY thanks the Institute Mittag Leffler for hospitality during his stay in the fall of 2012.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.LPMMC, UMR 5493Université Grenoble 1 and CNRSGrenobleFrance
  2. 2.UPMC Univ Paris 06, UMR 7598 Laboratoire Jacques-Louis LionsParisFrance
  3. 3.CNRS, UMR 7598 LJLLParisFrance
  4. 4.Courant InstituteNew York UniversityNew YorkUSA
  5. 5.Fakultät für PhysikUniversität WienViennaAustria
  6. 6.Erwin Schrödinger Institute for Mathematical PhysicsViennaAustria

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