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Recently, there have been significant new insights concerning the conditions under which closed systems equilibrate locally. The question of whether subsystems thermalize-if the equilibrium state is independent of the initial state-is, however, much harder to answer in general. Here, we consider a setting in which thermalization can be addressed: a quantum quench under a Hamiltonian whose spectrum is fixed and whose basis is drawn from the Haar measure. If the Fourier transform of the spectral density is small, almost all bases lead to local equilibration to the thermal state with infinite temperature. This allows us to show that, under almost all Hamiltonians that are unitarily equivalent to a local Hamiltonian, it takes an algebraically small time for subsystems to thermalize. [ABSTRACT FROM AUTHOR]

Non-equilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet consisting of N particles, can be found by solving an N-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta. [ABSTRACT FROM AUTHOR]