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Modeling and Computational Methods for Kinetic Equations pp 287–320Cite as

Birkhäuser

Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation

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Abstract

We review some modelling and numerical aspects in quantum kinetic theory for a gas of interacting bosons and we try to explain what makes Bose-Einstein condensation in a dilute gas mathematically interesting and numerically challenging. Particular care is devoted to the development of efficient numerical schemes for the quantum Boltzmann equation that preserve the main physical features of the continuous problem, namely conservation of mass and energy, the entropy inequality and generalized Bose-Einstein distributions as steady states. These properties are essential in order to develop numerical methods that are able to capture the challenging phenomenon of bosons condensation. We also show that the resulting schemes can be evaluated with the use of fast algorithms. In order to study the evolution of the condensate wave function the Gross-Pitaevskii equation is presented together with some schemes for its efficient numerical solution.

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Author information

Authors and Affiliations

  1. Department of Computational Science, National University of Singapore, 117543, Singapore

    Weizhu Bao

  2. Department of Mathematics, University of Ferrara, Via Machiavelli 35,4110 Ferrara, Italy

    Lorenzo Pareschi

  3. Department of Mathematics, University of Vienna, Boltzmanngasse 9, 1090 Vienna, Austria

    Peter A. Markowich

Authors
  1. Weizhu Bao
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  2. Lorenzo Pareschi
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  3. Peter A. Markowich
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Université Paul Sabatier, 31 062, Toulouse Cedex, France

    Pierre Degond

  2. Department of Mathematics, Università di Ferrara, I-44100, Ferrara, Italy

    Lorenzo Pareschi

  3. Università di Catania, 95125, Catania, Italy

    Giovanni Russo

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Bao, W., Pareschi, L., Markowich, P.A. (2004). Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation. In: Degond, P., Pareschi, L., Russo, G. (eds) Modeling and Computational Methods for Kinetic Equations. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8200-2_10

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  • DOI: https://doi.org/10.1007/978-0-8176-8200-2_10

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6487-3

  • Online ISBN: 978-0-8176-8200-2

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