Related papers: Crystallography Without Periodicity
Deformation K-theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2-periodic above the rational cohomological dimension of G…
Particle Physics in International Collaboration. Talk given at Kolloquiumstag ``125 Jahre Teilchenphysik in Aachen", October 1995
Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental…
Redundancies are pointed out in the widely used extension of the crystallographic concept of Bravais class to quasiperiodic materials. Such pitfalls can be avoided by abandoning the obsolete paradigm that bases ordinary crystallography on…
Crystallography has proven a rich source of ideas over several centuries. Among the many ways of looking at space groups, N. David Mermin has pioneered the Fourier-space approach. Recently, we have supplemented this approach with methods…
In this article we describe the crystallization conjecture. It states that, in appropriate physical conditions, interacting particles always place themselves into periodic configurations, breaking thereby the natural translation-invariance…
In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and…
This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in $2017$.
Non-periodic systems have become more important in recent years, both theoretically and practically. Their description via Delone sets requires the extension of many standard concepts of crystallography. Here, we summarise some useful…
Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at…
In 1965, I published a paper, exhibiting a hitherto unknown limit of the Lorentz group, which I christened Carroll group because of its seemingly paradoxical physical contents. Since I saw it as more curious than relevant, I published it in…
The compelling original idea of a time crystal has referred to a structure that repeats in time as well as in space, an idea that has attracted significant interest recently. While obstructions to realize such structures became apparent…
This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical…
Lecture given at the workshop "Mathematical aspects of theories of gravitation", Stefan Banach International Mathematical Centre, 7 March 1996. A mini-introduction to critical phenomena in gravitational collapse is combined with a more…
A Comment on "Space-Time Crystals of Trapped ions", by Tongcang Li et al. (PRL 109, 163001 (2012); arXiv:1206.4772
In a recent article [J. G. Wang, U. Dhumal, M. E. Zakhari, and R. N. Zia, AIChE Journal 72, e70275 (2026).], the authors discuss the absence of simulations of monodisperse hard spheres in which a metastable fluid spontaneously nucleates…
A critical examination is made of two simple implementations of the idea that cosmology can be viewed as a renormalization group flow. Both implementations are shown to fail when applied to a massless, minimally coupled scalar with a…
Lectures presented at the 42nd Scottish Universities Summer School in Physics, St. Andrews, Scotland, August 1993.
I review the holographic theory of space-time and its applications to cosmology. Much of this has appeared before, but the discussion is more unified and concise. I also include some material on work in progress, whose aim is to understand…
We assume that the Universe has a non trivial topology whose compact spatial sections have a volume significantly smaller than the horizon volume. By a topological lens effect, such a "folded" space configuration generates multiple images…