In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the
paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy
distribution after a quench is not related to standard statistical ensembles
and cannot explain thermalization. The latter is proposed to stem from what he
calls the eigenstate thermalization hypothesis and which boils down to the fact
that simple observables are expected to be smooth functions of the energy. In
this Reply, we show that there is no contradiction or confusion between the
observations and discussions of Roux and the expected thermalization scenario
discussed by Rigol. In addition, we emphasize a few other important aspects, in
particular the definition of temperature and the equivalence of ensemble, which
are much more difficult to show numerically even though we believe they are
essential to the discussion of thermalization. These remarks could be of
interest to people interested in the interpretation of the data obtained on
finite-size systems.Comment: 3 page
