Introduction to Non-Relativistic Transport Theories

  • C. Grégoire
Part of the NATO ASI Series book series (NSSB, volume 205)


We give an introduction to non-relativistic transport theories. In the first part, we show how kinetic equations can be derived from the BBGKY hierarchy. Maxwell models are briefly discussed. The hydrodynamical regime and the Chapman-Enskog solution for classical systems are reviewed. Applications to noble gases are given. We give an outline of the Boltzmann-Langevin method for dealing with fluctuations. The semi-classical description of nuclear systems is discussed by comparing TDHF simulations to Vlasov calculations. The second part is devoted to quantal non-relativistic systems. It is based on the Green’s function formalism. Special emphasis is given to the time-ordering method proposed by Keldysh. It is shown that a generalized Boltzmann equation can be obtained via smoothness arguments. This equation reduces to the semi-classical Landau-Vlasov equation in the quasi-particle approximation and the T-matrix approximation. Examples like the impurity scattering problem and Fermi liquids are given. It is argued that for nuclear systems as those encountered in heavy-ion collisions above 200–300 MeV/nucleon a proper account of the quantal effects in the collisional regime is required.


Boltzmann Equation Fermi Liquid Vlasov Equation Collision Term BBGKY Hierarchy 
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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • C. Grégoire
    • 1
    • 2
  1. 1.Physics DepartmentState University of New York at Stony BrookStony BrookUSA
  2. 2.GANILCaen,CedexFrance

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