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A question of phase density

  1. Jul 23, 2008 #1
    In the classical mechanics each system can be described by the phase density [tex]\rho(x,t)[/tex]
    , which is evolved by Liouville's equation.
    Recently I read a paper: Evidences of classical and quantum chaos in the time evolution of nonequilibrium ensembles (Y, Gu, PLA, 149, 95 (1990)). In it, it says that

    [tex]\int\rho(x,t)^{2} dx [/tex] is constant in time.
    But, as far as I know, due to the conservation of particles, [tex]\int\rho(x,t) dx [/tex]
    is constant in time.
    I don’t know how he got the conclusion?
     
    Last edited by a moderator: Jul 23, 2008
  2. jcsd
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