Lattices align in two dimensions

Spontaneous formation of domain wall lattices in two spatial dimensions

We show that the process of spontaneous symmetry breaking can trap a field theoretic system in a highly non-trivial state containing a lattice of domain walls. In one large compact space dimension, a lattice is inevitably formed. In two dimensions, the probability of lattice formation depends on the ratio of sizes Lx, Ly of the spatial dimensions. We find that a lattice can form even if R ≡ Ly/...

Coincidences of Hypercubic Lattices in 4 dimensions

We consider the CSLs of 4–dimensional hypercubic lattices. In particular, we derive the coincidence index Σ and calculate the number of different CSLs as well as the number of inequivalent CSLs for a given Σ. The hypercubic face centered case is dealt with in detail and it is sketched how to derive the corresponding results for the primitive hypercubic lattice.

Rounding Face Lattices in D Dimensions

On extremal lattices in jump dimensions

Let (L,Q) be an even unimodular lattice, so L is a free Z-module of rank n, and Q : L → Z a positive definite regular integral quadratic form. Then L can be embedded into Euclidean n-space (R, (, )) with bilinear form defined by (x, y) := Q(x + y) − Q(x) − Q(y) and L defines a lattice sphere packing, whose density measures its error correcting properties. One of the main goals in lattice theory...

Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions.

We experimentally and numerically investigate the expansion of initially localized ultracold bosons in homogeneous one- and two-dimensional optical lattices. We find that both dimensionality and interaction strength crucially influence these nonequilibrium dynamics. While the atoms expand ballistically in all integrable limits, deviations from these limits dramatically suppress the expansion an...