Holomorphic curves in exploded manifolds: regularity

The category of exploded manifolds is an extension of the category of smooth manifolds related to tropical geometry in which some adiabatic limits appear as smooth families. This paper studies the dbar equation on variations of a given family of curves in an exploded manifold. Roughly, we prove that the dbar equation on variations of an exploded family of curves behaves as nicely as the dbar equation on variations of a smooth family of smooth curves, even though exploded families of curves allow the development of normal crossing or log smooth singularities. The resulting regularity results are used in a series of separate papers to construct Gromov Witten invariants for exploded manifolds.Comment: 52 pages. v2: The construction of Gromov Witten invariants has been removed to another paper. v3: rewritten introduction, improved exposition. v4, v5: improved exposition v6, v7: Minor improvements and some expanded explanations, (including weakened hypothesis for Proposition 3.11), as suggested by an anonymous referee of a different paper. Final version to appear in Geometry and Topolog

Determining surface magnetization and local magnetic moments with atomic scale resolution

We propose a method to determine the direction of surface magnetization and local magnetic moments on the atomic scale. The method comprises high resolution scanning tunneling microscope experiments in conjunction with first principles simulations of the tunneling current. The potential of the method is demonstrated on a model system, antiferromagnetic Mn overlayers on W(110). We expect that it will ultimately allow to study the detailed changes of magnetic surface structures in the vicinity of dopants or impurities.Comment: Four pages (RevTeX) and five figures (EPS). For related papers see http://cmmp.phys.ucl.ac.uk/~wah

Shearer's point process, the hard-sphere model and a continuum Lov\'asz Local Lemma

A point process is R-dependent, if it behaves independently beyond the minimum distance R. This work investigates uniform positive lower bounds on the avoidance functions of R-dependent simple point processes with a common intensity. Intensities with such bounds are described by the existence of Shearer's point process, the unique R-dependent and R-hard-core point process with a given intensity. This work also presents several extensions of the Lov\'asz Local Lemma, a sufficient condition on the intensity and R to guarantee the existence of Shearer's point process and exponential lower bounds. Shearer's point process shares combinatorial structure with the hard-sphere model with radius R, the unique R-hard-core Markov point process. Bounds from the Lov\'asz Local Lemma convert into lower bounds on the radius of convergence of a high-temperature cluster expansion of the hard-sphere model. This recovers a classic result of Ruelle on the uniqueness of the Gibbs measure of the hard-sphere model via an inductive approach \`a la Dobrushin

Quantum mechanics: A new chapter?

We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Gr\"ossing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely due to the quantized interactions leading to a discrete set of transferred momenta. A separate experimental confirmation of this interpretation for double-slit interferometry of photons has been given by the group of Steinberg.Comment: 8 pages, article to appear in the Proceedings of the 6th Conference: Quantum Theory: Reconsideration of Foundations, June 11-14 2012 in Vaexjoe, Swede