Rigorous mean-field dynamics of lattice bosons: Quenches from the Mott insulator

Doped Mott insulator: Results from mean-field theory.

The interaction-driven metal-insulator transition has fascinated theorists and experimentalists for many years. This transition is named after Sir Nevill Mott, who laid down the foundations of our physical understanding of this phenomenon. A periodic system having an odd number of electrons per unit cell must be an insulator ~Mott insulator! when the electron-electron correlations are much larg...

Quantum phase transition from a Mott insulator to a superfluid in bosons

Bose Hubbard model is presented and basic natures of Mott insulating phase and superfluid phase are studied in this essay. Also how and when this quantum phase transition occurs is discussed. Experimental supports from ultracold atoms physics are explained, while some miscellaneous topics are touched in the end.

Superfluid to Mott Insulator transition in an optical lattice

Nonlinear quantum critical transport and the Schwinger mechanism for a superfluid-mott-insulator transition of bosons.

Scaling arguments imply that quantum-critical points exhibit universal nonlinear responses to external probes. We investigate the origins of such nonlinearities in transport, which is especially problematic since the system is necessarily driven far from equilibrium. We argue that for a wide class of systems the new ingredient that enters is the Schwinger mechanism--the production of carriers f...

Mean-field lattice trees

We introduce a mean-field model of lattice trees based on embeddings into Zd of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade, and provides an alternate approach to work of Aldous. The scaling limit of the mean-field model is integrated superBr...