Abstract
Motivated by recent experimental progress on measuring various correlation functions in systems of ultracold atoms in optical lattices, we study properties of the Bose-Hubbard model in external synthetic magnetic field to describe transport phenomena in a multiband strongly interacting bosonic systems. We calculate the conductivity both in the Mott insulator and superfluid phases and investigate its two main contributions: intra- and interband. It appears that the interband processes dominate the transport properties by at least an order of magnitude. Also, at finite temperatures, additional transport channels appear due to coupling of the thermally excited particles or holes to the external field.
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