Hydrodynamic long-time tails after a quantum quench

Abstract

After a quantum quench, a sudden change of parameters, generic many-particle quantum systems are expected to equilibrate. A few collisions of quasiparticles are usually sufficient to establish approximately local equilibrium. Reaching global equilibrium is, however, much more difficult as conserved quantities have to be transported for long distances to build up a pattern of fluctuations characteristic for equilibrium. Here we investigate the quantum quench of the one-dimensional bosonic Hubbard model from infinite to finite interaction strength $U$ using semiclassical methods for weak and exact diagonalization for strong quenches. Equilibrium is approached only slowly, as ${t}^{\ensuremath{-}1/2}$ with subleading corrections proportional to ${t}^{\ensuremath{-}3/4}$, consistent with predictions from hydrodynamics. We show that these long-time tails determine the relaxation of a wide range of physical observables.