Degenerate quantum gases

Participants

Amandine Aftalion (Organiser), James Anglin, Mikhail Baranov, Natalia Berloff, Xavier Blanc, Eric Cances, Jean Dalibard, Miguel Escobedo, Gero Friesecke, Philippe Gravejat, David Guéry-Odelin (Organiser), Robert Jerrard, Christophe Josserand, Georgios M. Kavoulakis, Allan Macdonald, Vincent Millot, Francis Nier, Yves Pomeau, Robert Seiringer, Florian Theil

 

Review

Degenerate quantum gases: Maths-Physics confrontation
by Amandine Aftalion and David Guéry-Odelin
7 – 13 July, 2005

The review being in French, hereafter are given the list of open problems and titles of talks:

Open problems:

  1. Tkachenko modes

What is expected ? Will it be different for Helium ? What is still expected experimentally or theoretically ? What theoretical results could help ?

  1. Correlation in BEC

N-body hamiltonian / GP: are there models in between in which correlation is taken into account ? What kind of phenomena are they able to describe ?

  1. Molecular condensates

Experimental state of the art : is it possible to condensate molecules or to form molecules in atomic condensates ?

What kind of mathematical models describe this phenomena ?

If so, can numerical simulations explain the experimental data and/or help in designing new experiments?

What is going on through Feschbach resonance ?

  1. Modelling of condensates

Give an ab initio account of a Bose-Einstein condensate : real atoms have interactions which admit bounds states. By constat, the interpretation of BECs as ground states appears to require interactions which do not admit ground states.

In what sense GP equation describes something else titan the condensate?

State of the art on the modelling of the formation and first stages of the condensate Finite temperature

If before the condensation, the distribution of particles is described by a kinetic Uehling-Uhlenbeck equation, and after the condensation, the system gas + condensate is described by a system kinetic + GP equations, is there a simple model describing the transition ?

Titles of talks:

  1. Amandine Aftalion (Laboratoire Jacques Louis Lions, Université Paris 6) -Introduction and open problems
  2. James Anglin (Center for ultracold atoms, MIT) – a) Fancy mathematics as a two-edged sword and b) Vortex matter
  3. Mikhail A.Baranov (Van der Waals-Zeeman Institute, University of Amsterdam) – Degenerate ferm-systems
  4. Natalia Berloff (DAMTP, Univ of Cambridge) – a) Mathematical models of superfluid turbulence & b) Solitary waves in Bose-Einstein condensates: from vortex rings to vortons and springs
  5. Xavier Blanc (Laboratoire Jacques Louis Lions, Université Paris 6) – Vortex lattices in fast rotating BEC
  6. Eric Cances (Cermics, Ecole des ponts et chaussées) —
  7. Jean Dalibard (Laboratoire Kastler Brossel, ENS) – Rotating Bose-Einstein condensates : experimental issues and results
  8. Miguel Escobedo (Universidad del Pais Vasco) – Singular solutions for homogeneous quantum kinetic equations
  9. Gero Friesecke (Mathematical Institute, University of Warwick) —
  10. Philippe Gravejat (Laboratoire Jacques Louis Lions, Université Paris 6) – Travelling waves for the Gross-Pitaevskii equation
  11. David Guéry-Odelin (Laboratoire Kastler Brossel, ENS) – Experiments versus theory on ultracold atoms
  12. Robert Jerrard (Département de Mathématiques, Université de Toronto) – Mathematical methods for vortex in Bose-Einstein condensates
  13. Christophe Josserand (Laboratoire de modélisation en mécanique, Université Paris 6) – Vortices in condensate mixtures
  14. Georgios M. Kavoulakis (LTH, MATFYS, Lund) – Solitary waves and vortex states in confined and cold gases of atoms
  15. Allan MacDonald (Department of Physics, The University of Texas at Austin) – Condensed matter physics
  16. Vincent Millot (Laboratoire Jacques Louis Lions, Université Paris 6) – Vortex patterns for 2D Bose-Einstein condensates in rotating traps
  17. Francis Nier (IRMAR,Rennes) – LLL problem and Bargman spaces
  18. Yves Pomeau (Laboratoire de Physique Statistique, ENS) – Boundary conditions in real superflows : surface roughness and the Landau critical speed
  19. Robert Seiringer (Département de Physique, Jadwin) – a) Dilute trapped Bose gases : Rigourous results on the many-body problem & b) Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
  20. Florian Theil (Mathematical Institute, University of Warwick) – Periodicity of groundstates

Read the review in French

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