  We study a one-dimensional interacting Bose gas periodically kicked. In
absence of interactions, it is well known that this system dynamically
localizes, i.e. the system reaches a steady-state where the energy saturates
and the single-particle wave-functions are exponentially localized in momentum
space. Focusing on the Tonks (strongly interacting) regime, we study the
many-body dynamically localized steady-state of a kicked Bose gas. We show that
this steady-state is ergodic, i.e. described by a thermal density matrix, with
an effective temperature that depends on the kicking parameters and the number
of particles. The one-body reduced density matrix of the gas decays
exponentially at large distance, implying absence of coherence, while the
momentum distribution's tail at large momenta is characterized by an
effectively thermal Tan contact.
