Hyperbolic Unit Groups and Quaternion Algebras

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.Comment: 15 pages, this work is part of the PHd. Thesis of the third author. The paper was accepted in Proceedings Mathematical Science

Quantum Properties of a Which-Way Detector

We explore quantum properties of a which-way detector using three versions of an idealized two slit arrangements. Firstly we derive complementarity relations for the detector; secondly we show how the "experiment" may be altered in such a way that using single position measurement on the screen we can obtain quantum erasure. Finally we show how to construct a superposition of "wave" and "particle" components