Correlation functions for a strongly coupled boson system and plane partitions.

A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q-boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit.

Boundary polarization in the six-vertex model.

Vertical-arrow fluctuations near the boundaries in the six-vertex model on the two-dimensional NxN square lattice with the domain wall boundary conditions are considered. The one-point correlation function ("boundary polarization") is expressed via the partition function of the model on a sublattice. The partition function is represented in terms of standard objects in the theory of orthogonal polynomials.

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.