- #1
xylai
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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: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-46S5C37-24M&_user=6104324&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000069295&_version=1&_urlVersion=0&_userid=6104324&md5=d41e737ddc2514dbbeca4a99047e66f7"(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?
, which is evolved by Liouville's equation.
Recently I read a paper: http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-46S5C37-24M&_user=6104324&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000069295&_version=1&_urlVersion=0&_userid=6104324&md5=d41e737ddc2514dbbeca4a99047e66f7"(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?
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