13-17 December 2010

**Organisers**: Professor S Jin (*Wisconsin*) and Professor PA Markowich (*Cambridge*).

In association with the Newton Institute programme Partial Differential Equations in Kinetic Theories (16 August - 22 December 2010)

Poster Session | Programme | Participants | Application | Accommodation and Costs | Group Photograph

Quantum fluid modelling has attracted a lot of recent attention, mainly due to the exiting experimental discoveries in Bose-Einstein condensation of the last decade which may have possible applications in quantum computing. Typically, modelling is based on nonlinear Schrodinger equations, like the cubically nonlinear Gross-Pitaevskii equation describing the evolution of Bose-Einstein condensates. Topics of interest include vortex dynamics and vortex pattern, mixing of scales in random phase approximations (related to turbulence theory), lattice condensates and multi-component condensates modelled by coupled systems of nonlinear Schrodinger equations. Kinetic equations, relying mainly on the Wigner transformation, can also be applied to quantum fluid dynamics. Recently hybrid kinetic-quantum mechanical models, coupling the Gross-Pitaevskii equation to the boson Boltzmann equation also have become a topic of strong interest. Many deep and open mathematical problems arise in connection with the boson Boltzmann equation in the spatially inhomogeneous case, due to the weak growth of the entropy functional which may even permit the occurence of singularities in finite time. New efficient numerical methods for quantum Boltzmann equations, and their validity in the quantum hydrodynamic regimes, accurate simulations crossing the regimes from the Gross-Pitaevski equation to the quantum Boltzmann equations, efficient Bloch decomposition based numerical methods for quantum dynamics in periodic and random media, are also important research directions to be pursued in this programme.

- Alexandre, R (
*Université d'Evry-Val-d'Essonne*) - Antonelli, P (
*Cambridge*) - Bao, W (
*National University of Singapore*) - Bardos, C (
*Université Paris 7 - Denis-Diderot*) - Berloff, N (
*Cambridge*) - Carles , R (
*Université Montpellier 2*) - Dolbeault, J (
*Université Paris-Dauphine*) - Fibich, G (
*Tel Aviv University*) - Filbet, F (
*Université Claude Bernard Lyon 1*) - Gasser, I (
*Universität Hamburg*) - Hintermueller, H (
*Humboldt Universität zu Berlin*) - Huang, Z (
*Tsinghua University*) - Juengel, A (
*Technical University of Vienna*) - Klein, C (
*Université de Bourgogne*) - Lasser, C (
*Free University of Berlin*) - Méhats, F (
*Université de Rennes 1*) - Paul, T (
*École Polytechnique*) - Saut, J C (
*Université Paris-Sud 11*) - Schirmer, S (
*Cambridge*) - Sparber, C (
*Cambridge*) - Weishaeupl, R-M (
*Universität Wien*) - Wu, H (
*Tsinghua University*) - Zheng, C (
*Tsinghua University*)

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