Chaos, Ergodization, and Thermalization with Few-Mode Bose-Einstein Condensates

I describe two minimal Bose-Hubbard models which exhibit classical chaos and demonstrate its relation to phase space ergodization and thermalization. The first model is a realization of a kicked top via driving of the mode-coupling term in a Bose-Hubbard dimer. Coherent preparations in the chaotic phase-space regions of this model constitute far-from-equilibrium wavepackets with Floquet participation numbers which scale linearly with the size of the Hilbert space. Consequently, such preparations exhibit ergodization and effectively loose their one-particle coherence irreversibly, as compared to the collapse and revival dynamics obtained for coherent preparations in the integrable dimer limit. The second model is a Bose-Hubbard trimer which is the minimal system for obtaining chaos without driving. Considering two weakly coupled trimers, thermalization between them is attained via the linear diffusive response of each subsystem to the effective drive exerted on it by the other. This energy diffusion is captured well by a Fokker Planck equation, which implies thermodynamical Einstein relations.