Related papers: Atoms and coatoms in three-generated lattices
We investigate the effect of the anisotropy between the s-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
The set of permutations on a finite set can be given a lattice structure (known as the weak Bruhat order). The lattice structure is generalized to the set of words on a fixed alphabet $\Sigma = \{ x, y, z, ... \}$, where each letter has a…
The phase diagram of binary mixtures of particles interacting via a pair potential of parallel dipoles is computed at zero temperature as a function of composition and the ratio of their magnetic susceptibilities. Using lattice sums, a rich…
Let $M$ be a cancellative and commutative monoid (written additively). The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements (often called atoms in the literature). Weaker versions of…
The positions of atoms forming a carbon nanotube are usually described by using a system of generators of the symmetry group. Each atomic position corresponds to an element of the set Z X {0,1,...,n} X {0,1}, where n is a natural number…
We study the entangled states that can be generated using two species of atoms trapped in independently movable, two-dimensional optical lattices. We show that using two sets of measurements it is possible to measure a set of entanglement…
Let $M$ be a $3$-connected matroid. A pair $\{e,f\}$ in $M$ is detachable if $M \backslash e \backslash f$ or $M / e / f$ is $3$-connected. Williams (2015) proved that if $M$ has at least 13 elements, then at least one of the following…
We introduce maximal and average coherence on lattices by analogy with these notions on frames in Euclidean spaces. Lattices with low coherence can be of interest in signal processing, whereas lattices with high orthogonality defect are of…
We prove an identity for five arguments, valid in the lattice of natural numbers with gcd and lcm as lattice operations. More generally, this identity characterizes arbitrary distributive lattices. Fixing three of the five arguments, we…
Recent experiments demonstrate the ability to construct cold atom mixtures with species selective optical lattices. This allows for the possibility of a mixed-dimension system, where one fermionic atomic species is confined to a two…
Let $K$ be a convex body in $\mathbb{R}^n$, let $L$ be a lattice with covolume one, and let $\eta>0$. We say that $K$ and $L$ form an $\eta$-smooth cover if each point $x \in \mathbb{R}^n$ is covered by $(1 \pm \eta) vol(K)$ translates of…
We present linear ensembles of dangling bond chains on a hydrogen terminated Si(100) surface, patterned in the closest spaced arrangement allowed by the surface lattice. Local density of states maps over a range of voltages extending…
The carbon atom provides the backbone for the complex organic chemistry composing the building blocks of life. The physics of the carbon nucleus in its predominant isotope, $^{12}$C, is similarly full of multifaceted complexity. Some…
New series of $2^{2m}$-dimensional universally strongly perfect lattices $\Lambda_I $ and $\Gamma_J $ are constructed with $$2BW_{2m} ^{\#} \subseteq \Gamma _J \subseteq BW_{2m} \subseteq \Lambda _I \subseteq BW _{2m}^{\#} .$$ The lattices…
In the past, light-assisted cold collisions between laser cooled atoms have been widely studied in magneto-optical atom traps (MOTs). We describe here theoretical studies of dynamical interactions, specifically cold collisions, between…
We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d…
Ultracold gases in optical lattices are of great interest, because these systems bear a great potential for applications in quantum simulations and quantum information processing, in particular when using particles with a long-range…
A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and…
Optical lattices are typically created via the ac-Stark shift, which are limited by diffraction to periodicities $\ge\lambda/2$, where $\lambda$ is the wavelength of light used to create them. Lattices with smaller periodicities may be…