2006/07/05 by Kristan Temme, Thomas Gasenzer · 16 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Hamiltonian (control theory) #Inverse #Lattice (music) #Mathematical physics #Mathematics #Non-equilibrium thermodynamics #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #cond-mat.other
paper · pdf · doi:10.1103/physreva.74.053603
published in Physical Review A 74(5) (American Physical Society) · 9 pages RevTeX, 3 figures
arxiv created 2006/07/05 · openalex publication_date 2006/11/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a case where the gas is strongly interacting. This is realized by an appropriate choice of the parameters in the Hamiltonian, and by starting with an initial state, where one lattice well contains a Bose-Einstein condensate while all other wells are empty. Oscillations of the condensate as well as noncondensate fractions of the gas between the different sites of the lattice are found to be damped as a consequence of the collisional interactions between the atoms. Functional integral techniques involving self-consistently determined mean fields as well as two-point correlation functions are used to derive the two-particle-irreducible (2PI) effective action. The action is expanded in inverse powers of the number of field components N, and the dynamic equations are derived from it to next-to-leading order in this expansion. This approach reaches considerably beyond the Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the exact quantum dynamics obtained by Rey et al. [Phys. Rev. A 69, 033610 (2004)] for small atom numbers.