Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-André model which can cause local...

The effect of interaction of low-index atomic planes, (100), (110), and (111) terminating CdSe platelet nanocrystals is examined using molecular dynamics (MD) simulations. Asymmetry of the environment of atoms at the end surface layers leads to anisotropic deformation of the cubic lattice and to a relative shift of Cd and Se sub-lattices. Interference of distortions of the crystal lattice origi...

Introduction. For'several years one of the outstanding problems of lattice theory has been the following: Is every lattice with unique complements a Boolean algebra? Any number of weak additional restrictions are sufficient for an affirmative answer. For example, if a lattice is modular (G. Bergman [l](1)) or ortho-complemented (G. Birkhoff [l]) or atomic (G. Birkhoff and M. Ward [l]), then uni...

We report the experimental observation of a lensing effect on a Bose-Einstein condensate expanding in a moving 1D optical lattice. The effect of the periodic potential can be described by an effective mass dependent on the condensate quasimomentum. By changing the velocity of the atoms in the frame of the optical lattice, we induce a focusing of the condensate along the lattice direction. The e...

The stability and failure mechanism of a structure at the nanometer scale are important for understanding the mechanical behavior of nanoscale materials and structures. This thesis focuses on the material stability of atomic structures. First, the material stability of pristine carbon nanotubes is investigated at the continuum level by using the crystal elasticity theory. A homogenized continuu...

Ausführungen, die wörtlich oder sinngemäÿ übernommen wurden, sind als solche gekennzeichnet. The lubrication force is an important problem in simulations of suspended particles with the lattice Boltzmann method. When two particles approach each other and get near contact, closer than the lattice spacing, the thin layer of uid, still left between the particles, cannot be suciently simulated, whi...

In the paper we investigate Birkhoff’s conditions (Bi) and (Bi∗). We prove that a discrete lattice L satisfies the condition (Bi) (the condition (Bi∗)) if and only if L is a 4-cell lattice not containing a cover-preserving sublattice isomorphic to the lattice S∗ 7 (the lattice S7). As a corollary we obtain a well known result of J. Jakub́ık from [6]. Furthermore, lattices S7 and S ∗ 7 are consid...

An element s of an (abstract) algebra A is a single element of A if asb = 0 and a, b ∈ A imply that as = 0 or sb = 0. Let X be a real or complex reflexive Banach space, and let B be a finite atomic Boolean subspace lattice on X, with the property that the vector sum K +L is closed, for every K,L ∈ B. For any subspace lattice D ⊆ B the single elements of Alg D are characterised in terms of a coo...