  We study the time-dependence of the magnetization profile, m_l(t), of a large
finite open quantum Ising chain after a quench. We observe a cyclic variation,
in which starting with an exponentially decreasing period the local
magnetization arrives to a quasi-stationary regime, which is followed by an
exponentially fast reconstruction period. The non-thermal behavior observed at
near-surface sites turns over to thermal behavior for bulk sites. Besides the
standard time- and length-scales a non-standard time-scale is identified in the
reconstruction period.
