Reply to "Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined' ''

TL;DR

This paper clarifies misconceptions about thermalization in quantum many-body systems, emphasizing the importance of ensemble equivalence and temperature definitions, and discusses their relevance to finite-size system data interpretation.

Contribution

It resolves apparent contradictions between previous studies on thermalization, highlighting the significance of ensemble definitions and temperature in understanding quantum quench dynamics.

Findings

No contradiction between Roux and Rigol's observations.

Ensemble equivalence and temperature definitions are crucial for thermalization analysis.

Finite-size systems require careful interpretation of thermalization data.

Abstract

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.