Exact analysis of prethermalization of a coherently split one-dimensional Bose gas

We theoretically study the prethermalization dynamics of a coherently split one-dimensional Bose gas by using the Bethe ansatz method. Prethermalization is a relaxation process to a quasi-stationary state before reaching the true equilibrium state. The concept of prethermalization is important for understanding the fundamental aspects of quantum statistical mechanics such as ``equilibration'' and ``relaxation'' in isolated quantum many-body systems. Prethermalization and its connection to integrability in one-dimensional quantum systems have been intensively studied by both experiments and theories. For instance, M. Gring et al. recently observed the evolution of a rapidly and coherently split one-dimensional Bose gas for large numbers of particles and compare the evolution of the system to the prediction of the Tomonaga-Luttinger liquid (TLL) theory. Here we employ the Bethe ansatz method and precisely analyze the prethermalization process over a long-time scale beyond the TLL prediction.