Non-Equilibrium Dynamics in Ultracold Atoms: A Projection Operator Approach

Sengupta Krishnendu

Abstract


In this article we provide a brief pedagogical introduction tothe physics of the Bose-Hubbard model near its superfluid-insulator transition.We focus on the properties of the system near this quantum criticalpoint in the presence of an external drive which constitutes a ramp of thehopping strength J of the bosons with a fixed rate τ−1. We provide anintroduction to the projection operator method which can treat such nonequlibriumdynamics of the model beyond mean-field theory and discussits relevance for current experiments.

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