When a quantum many-body system undergoes a quench, the time-averaged density matrix $\overline{\rho }$ governs the time-averaged expectation value of any observable. It is therefore the key object to look at when comparing results with equilibrium predictions. We show that the weights of $\overline{\rho }$ can be efficiently computed with Lanczos diagonalization for relatively large Hilbert spaces. As an application, we investigate the crossover from perturbative to nonperturbative quenches in the nonintegrable Bose-Hubbard model: in finite systems, an approximate Boltzmann distribution is observed for small quenches, while for larger ones the distributions do not follow standard equilibrium predictions. Studying thermodynamical features, such as the energy fluctuations and the entropy, show that $\overline{\rho }$ bears a memory of the initial state.

• Received 23 October 2008

DOI:https://doi.org/10.1103/PhysRevA.79.021608