Related papers: Finite atomic lattices and their monomial ideals
A mixture of light and heavy spin-polarized fermionic atoms in an optical lattice is considered. Tunneling of the heavy atoms is neglected such that they are only subject to thermal fluctuations. This results in a complex interplay between…
We study bosonic atoms in small optical lattices by exact diagonalization and observe a striking similarity to the superfluid to Mott insulator transition in macroscopic systems. The momentum distribution, the formation of an energy gap,…
Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…
The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic…
Lattice effective field theory applies the principles of effective field theory in a lattice framework where space and time are discretized. Nucleons are placed on the lattice sites, and the interactions are tuned to replicate the observed…
We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest…
We propose a scheme to realize lattice potentials of sub-wavelength spacing for ultracold atoms. It is based on spin-dependent optical lattices with a time-periodic modulation. We show that the atomic motion is well described by the…
We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…
Lattices of compatibly embedded finite fields are useful in computer algebra systems for managing many extensions of a finite field $\mathbb{F}_p$ at once. They can also be used to represent the algebraic closure $\bar{\mathbb{F}}_p$, and…
For ultracold and Bose-condensed atoms contained in periodic optical potential wells the quantized nature of their motion is clearly visible. The motion of the atomic wavepacket can also be accurately controlled. For those systems the…
Fermionic atoms in an optical superlattice can realize a very peculiar Anderson lattice model in which impurities interact with each other through a discretized set of delocalized levels. We investigate the interplay between Kondo effect…
In an earlier paper (math.NT/9906019) we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A "characteristic vector" of L is a vector w in L such that…
This is the third in a series of papers dealing with the algebraic theory of infinite classical lattices. This paper presents a theory of single measurements on a lattice which we represent as comprising a finite subvolume--the system of…
All experiments with ultracold atoms are performed in the presence of background residual gas. With the help of a suitable master equation we investigate a role of these fast atoms on the loss of coherence in optical lattices. We present an…
We propose an easy to use model to solve for interacting atoms in an optical lattice. This model allows for the whole range of weakly to strongly interacting atoms, and it includes the coupling between relative and center-of-mass motion via…
The concept of a $\lambda$-lattice was introduced by V. Sn\'a\v sel in order to generalize some lattice concepts for directed posets whose elements need not have suprema or infima. We extend the concept of semimodularity from lattices to…
We investigate atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices in the limit of strong atom-atom interactions. We derive the effective Hamiltonian describing the dynamics of the system and discuss its low temperature…
Part B (of a project involving four Parts) is about "bases of lines", a concept introduced by C. Herrmann and the author in the late 80's. Bases of lines attempt to describe a given modular lattice in a geometric way akin to how projective…
Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…
We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them,…