# A question of phase density

1. Jul 23, 2008

### xylai

In the classical mechanics each system can be described by the phase density $$\rho(x,t)$$
, 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

$$\int\rho(x,t)^{2} dx$$ is constant in time.
But, as far as I know, due to the conservation of particles, $$\int\rho(x,t) dx$$
is constant in time.
I don’t know how he got the conclusion?

Last edited by a moderator: Jul 23, 2008