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We study the dynamics of phase transitions in the one dimensionalBose-Hubbard model. To drive the system from Mott insulator to superfluidphase, we change the tunneling frequency at a finite rate. We investigate thebuild up of correlations during fast and slow transitions using variationalwave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, andnumerical simulations. We show that time-dependent correlations satisfycharacteristic scaling relations that can be measured in optical latticesfilled with cold atoms.Comment: 7+ pages, the Bogolubov section is completely rewritte

Dynamics of the Bose-Hubbard model: Transition from a Mott insulator to a superfluid