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

  • Weizhu Bao
  • Lorenzo Pareschi
  • Peter A. Markowich
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


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.


Boltzmann Equation Collision Operator Trapping Potential Ground State Solution Nonlinear Schrodinger Equation 


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Weizhu Bao
    • 1
  • Lorenzo Pareschi
    • 2
  • Peter A. Markowich
    • 3
  1. 1.Department of Computational ScienceNational University of SingaporeSingapore
  2. 2.Department of MathematicsUniversity of FerraraItaly
  3. 3.Department of MathematicsUniversity of ViennaAustria

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