Third-order phase transition in random tilings

We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size, reaches the arctic ellipse-the phase separation curve of the original (unmodified) Aztec diamond. We obtain this result by studying the thermodynamic limit of a certain nonlocal correlation function of the underlying six-vertex model with domain wall boundary conditions, the so-called emptiness formation probability (EFP). We consider EFP in two different representations: as a τ function for Toda chains and as a random matrix model integral. The latter has a discrete measure and a linear potential with hard walls; the observed phase transition shares properties with both Gross-Witten-Wadia and Douglas-Kazakov phase transitions.

Quantum dynamics of strongly interacting boson systems: atomic beam splitters and coupled Bose-Einstein condensates

An effective boson Hamiltonian applicable to atomic beam splitters, coupled Bose-Einstein condensates, and optical lattices can be made exactly solvable by including all n-body interactions. The model can include an arbitrary number of boson components. In the strong interaction limit the model becomes a quantum phase model, which also describes a tight-binding lattice particle. Through exact results for dynamic correlation functions, it is shown how the previous weak interaction dynamics of these systems are extended to strong interactions, now becoming relevant in the experiments. The effect of the number of boson components is also analyzed.