Relaxation dynamics of ultracold bosons in a double-well potential: Thermalization and prethermalization in a nearly integrable model

TL;DR

This study numerically examines how ultracold bosons in a double-well potential relax after a quench, revealing thermalization, prethermalization, and energy-dependent equilibration behaviors in a nearly integrable, nonchaotic quantum system.

Contribution

It demonstrates thermalization and prethermalization phenomena in a nearly integrable model of ultracold bosons, highlighting energy-dependent relaxation regimes and the role of eigenstate delocalization.

Findings

System exhibits thermalization consistent with ETH.

Prethermalization occurs at higher energies with longer metastable states.

Relaxation dynamics depend on initial energy and state delocalization.

Abstract

We numerically investigate the relaxation dynamics in an isolated quantum system of interacting bosons trapped in a double-well potential after an integrability breaking quench. Using the statistics of the spectrum, we identify the postquench Hamiltonian as nonchaotic and close to integrability over a wide range of interaction parameters. We demonstrate that the system exhibits thermalization in the context of the eigenstate thermalization hypothesis (ETH). We also explore the possibility of an initial state to delocalize with respect to the eigenstates of the postquench Hamiltonian even for energies away from the middle of the spectrum. We observe distinct regimes of equilibration process depending on the initial energy. For low energies, the system rapidly relaxes in a single step to a thermal state. As the energy increases towards the middle of the spectrum, the relaxation dynamics exhibits prethermalization and the lifetime of the metastable states grows. Time evolution of the occupation numbers and the von Neumann entropy in the mode-partitioned system underpins the analyses of the relaxation dynamics.