We numerically investigate the relaxation dynamics in an isolated quantumsystem of interacting bosons trapped in a double-well potential after anintegrability breaking quench. Using the statistics of the spectrum, weidentify the postquench Hamiltonian as nonchaotic and close to integrabilityover a wide range of interaction parameters. We demonstrate that the systemexhibits thermalization in the context of the eigenstate thermalizationhypothesis (ETH). We also explore the possibility of an initial state todelocalize with respect to the eigenstates of the postquench Hamiltonian evenfor energies away from the middle of the spectrum. We observe distinct regimesof equilibration process depending on the initial energy. For low energies, thesystem rapidly relaxes in a single step to a thermal state. As the energyincreases towards the middle of the spectrum, the relaxation dynamics exhibitsprethermalization and the lifetime of the metastable states grows. Timeevolution of the occupation numbers and the von Neumann entropy in themode-partitioned system underpins the analyses of the relaxation dynamics.
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