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The dynamical evolution of a Bose-Einstein condensate trapped in aone-dimensional lattice potential is investigated theoretically in theframework of the Bose-Hubbard model. The emphasis is set on thefar-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 aBose-Einstein condensate while all other wells are empty. Oscillations of thecondensate as well as non-condensate fractions of the gas between the differentsites of the lattice are found to be damped as a consequence of the collisionalinteractions between the atoms. Functional integral techniques involvingself-consistently determined mean fields as well as two-point correlationfunctions are used to derive the two-particle-irreducible (2PI) effectiveaction. The action is expanded in inverse powers of the number of fieldcomponents N, and the dynamic equations are derived from it to next-to-leadingorder in this expansion. This approach reaches considerably beyond theHartree-Fock-Bogoliubov mean-field theory, and its results are compared to theexact quantum dynamics obtained by A.M. Rey et al., Phys. Rev. A 69, 033610(2004) for small atom numbers.Comment: 9 pages RevTeX, 3 figure

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Nonequilibrium dynamics of condensates in a lattice with the two-particle-irreducible effective action in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mi mathvariant="script">N</mml:mi></mml:mrow></mml:math>expansion

Nonequilibrium dynamics of condensates in a lattice with the two-particle-irreducible effective action in the1∕Nexpansion