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e formulate a method for studying the quantum field dynamics of ultracoldBose gases confined within optical lattice potentials, within the lowestBloch-band Bose-Hubbard model. Our formalism extends the two-sites results ofPhys. Rev. Lett. {\bf86}, 000568 (2001) to the general case of $M$ latticesites. The methodology is based on mapping the Bose-Hubbard Hamiltonian to an$SU(M)$ pseudospin problem and truncating the resulting hierarchy of dynamicalequations for correlation functions, up to pair-correlations between $SU(M)$generators. Agreement with few-site exact many-particle calculations isconsistently better than the corresponding Hartree-Fock-Bogoliubovapproximation. Moreover, our approximation compares favorably with a moreelaborate two-particle irreducible effective action formalism, at a fraction ofthe analytic and numerical effort.Comment: 8 pages, 7 figure

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

Erratum: Quantum dynamics of Bose-Hubbard Hamiltonians beyond the Hartree-Fock-Bogoliubov approximation: The Bogoliubov back-reaction approximation [Phys. Rev. A<b>75</b>, 013613 (2007)]

Erratum: Quantum dynamics of Bose-Hubbard Hamiltonians beyond the Hartree-Fock-Bogoliubov approximation: The Bogoliubov back-reaction approximation [Phys. Rev. A75, 013613 (2007)]