In this paper we prove the following conclusions: (1). If E is a complete atomic lattice effect algebra, then E is (o)-continuous ⇔ E is order-topological ⇔ E is a totally order-disconnected ⇔ E is algebraic. (2). If E is a complete atomic distributive lattice effect algebra, then its Frink ideal topology τid is Hausdorff topology and is finer than its order topology τo, and τid = τo ⇔ 1 is fin...

Stimulated by recent progress in atom manipulation technology, the electronic properties of periodic structures artificially created with atoms on a substrate surface are studied, where constituent atoms are isolated from substrate atoms and interact with one another through neighboring-atom interactions. By reducing the lattice constant from infinity, the neighboring-atom interaction is gradua...

The snapshot object is an important tool for constructing wait-free asynchronous algorithms. We relate the snapshot object to the lattice agreement decision problem. It is shown that any algorithm for solving lattice agreement can be transformed into an implementation of a snapshot object. The overhead cost of this transformation is only a linear number of operations on atomic single-writer mul...

We consider designs of optical lattice clocks in view of the quantum statistics, relevant atomic spins, and atom-lattice interactions. The first two issues lead to two optimal constructions for the clock: a one-dimensional (1D) optical lattice loaded with spin-polarized fermions and a 3D optical lattice loaded with bosons. By taking atomic multipolar interactions with the lattice fields into ac...

We report the observation of strongly damped dipole oscillations of a quantum degenerate 1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is significant for very shallow axial lattices (0.25 photon recoil energies), and increases dramatically with increasing lattice depth, such that the gas becomes nearly immobile for times an order of magnitude longer than the s...

We present an atomic scale theory of lattice distortions using strain-related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at several length scales. We apply the approach to a two-dimensional square lattice with a monatomic basis and find the elastic deformations and hierarchical atomi...

Atomic structure models of multi-principal-element alloys (or high-entropy alloys) composed of four to eight componential elements in both BCC and FCC lattice structures are built according to the principle of maximum entropy. With the concept of entropic force, the maximum-entropy configurations of these phases are generated through the use of Monte Carlo computer simulation. The efficiency of...

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensi...