Realizability toposes and ordered PCA's

Partial combinatory algebras (pca's, for short), are well-known to form the basic ingredient for the construction of various realizability toposes, of which the Eective Topos is undoubtedly the most famous. There is more than one way to present the realizability topos associated to a pca; one may take the exact completion of the category of partitioned assemblies (see [7]), or one can use tripos theory. Triposes built from pca's are, together with those from locales, the most important and most extensively studied instances of triposes, but from a structural point of view, there are important dierences between the two; whereas locales are organized in a well-behaved category, which is a re ective subcategory of the category of toposes, it is not immediately clear what an appropriate category for pca's may look like. Moreover, there are various nice properties in the localic case, such as the fact that there is a one-to-one correspondence between maps of locales and geometric morphisms between the corresponding sheaf toposes, and also the fact that this correspondence preserves epi-mono factorizations; such anintimate connection is absent for pca's

Ultracold atoms in optical lattices

Bosonic atoms trapped in an optical lattice at very low temperatures, can be modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson approach for dealing with the Bose-Hubbard model, which enables us to analytically describe the physics of this model at nonzero temperatures. With our approach the phase diagram for this model at nonzero temperatures can be quantified.Comment: 29 pages, 10 figure

Modelling and experiments of self-reflectivity under femtosecond ablation conditions

We present a numerical model which describes the propagation of a single femtosecond laser pulse in a medium of which the optical properties dynamically change within the duration of the pulse. We use a Finite Difference Time Domain (FDTD) method to solve the Maxwell's equations coupled to equations describing the changes in the material properties. We use the model to simulate the self-reflectivity of strongly focused femtosecond laser pulses on silicon and gold under laser ablation condition. We compare the simulations to experimental results and find excellent agreement.Comment: 11 pages, 8 figure