the localization of the core exactly at $x=0$ and a sharp boundary of the container.](fig6.eps){width=".45\textwidth"}

To summarize, for all the quantities considered, we observed no systematic deviations between the MF theory and the MD data.

Collapse
========

According to the MF theory, if the energy of the uniform state becomes lower than $\e_{coll}\approx-0.339$, the system should undergo a collapse to a core-halo state. To study the collapse, we considered several uniform systems with the energies ranging between $\e=-0.5$ and $\e=-0.3$. The systems were initialized according to the MF density distributions. For systems with $\e<\e_{coll}$ the particles were distributed according to the MF density profile for $\e_{coll}$.

In a perfect agreement with the MF theory, a uniform state with $\e<\e_{coll}$ undergoes a gradual transition to a core-halo state with a typical timescale of $\t_{coll}\sim 10^4$ for $N=125$ – 250 particles. An example of the time dependence of the kinetic energy and the virial variable for a collapsing system is shown in Fig. \[fig\_coll\].

![\[fig\_coll\] Time dependence of the kinetic energy $\e_{kin}$ (top) and the virial variable $\s$ (bottom) of the collapsing uniform state with $\e=-0.5$ and $N=125$. The dashed horizontal lines indicate the equilibrium values of $\e_{kin}$ and $\s$ of the 