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In this work we study the time evolution of soft core bosons on aone-dimensional lattice, where the particles are initially quenched into aatomic density wave. At time $t=0$ the particles are released from the quenchand can evolve under the dynamics of a soft-core Bose-Hubbard Hamiltonian on alattice including a confining trap.

On the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas