Related papers: Crystallography Without Periodicity
Talk given by one of us (A. Zee) at Murray Gell-Mann's 80th Birthday Celebration held in Singapore, February 2010. Based on R. A. Porto and A. Zee, Class. Quant. Grav. 27, 065006 (2010) [arXiv:0910.3716 [hep-th]]
We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge…
Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…
\def\spose#1{\hbox to 0pt{#1\hss}} \def\lta{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}} \raise 2.0pt\hbox{$\mathchar"13C$}}} Groups of galaxies are highly linked to cosmology: 1) groups are tidally destroyed by the tidal field of the…
Difficulties around the idea of spontaneous breaking of time translation symmetry in a closed quantum mechanical system are identified, and then overcome in a simple model. The possibility of ordering in imaginary time is also discussed.
We propose a holographic formalism for a timelike entanglement entropy in non-conformal theories. This pseudoentropy is a complex-valued measure of information, which, in holographic non-conformal theories, receives contributions from a set…
The relation between the notion of crystalline symmetry and characteristic time intervals when this symmetry could be observed is analyzed. Several time scales are shown to exist for a system of interacting particles. It is only when the…
In recent years there has been some progress in the understanding of the global structure of stationary black hole space-times. In this paper we review some new results concerning the structure of stationary black hole space-times. In…
This is an unchanged version of an unpublished, ``state of the art'' survey given at a conference held in Stuttgart in 2001 to celebrate the 100th birthday of Richard Brauer. This text was recently quoted in several papers on the…
For Encyclopedia of Complexity and Systems Science (Springer Verlag). No abstract. I. Definition and Introduction II. Methods III. Quantities and Exponents IV. Fractal Dimension; Incipient Infinite Cluster V. Simple Renormalisation Group…
A summary of the session on Particle Astrophysics at the Rencontre de Vietnam, 2006.
Summary of a talk at the conference The Chaotic Universe in Rome, Feb, 1999
In the note by Khemani et al. [arXiv:2001.11037] the authors express conceptual disagreement with our recent paper on quantum time crystals [Phys. Rev. Lett. 123, 210602]. They criticise the idealized nature of the considered quantum time…
In a recent publication [Phys. Rev. Lett. {\bf 124}, 178902] \"Ohberg and Wright claim that in a chiral soliton model it is possible to realize a genuine time crystal which corresponds to a periodic evolution of an inhomogeneous probability…
The crystalline period map is a tool for linearizing $p$-divisible groups. It has been applied to study the Langlands correspondences, and has possible applications to the homotopy groups of spheres. The original construction of the period…
I present arguments indicating the impossibility of spontaneously rotating quantum timecrystals, as recently proposed by Frank Wilczek [arXiv:1202.2539]. In particular, I prove a No-Go Theorem, rigorously ruling out the possibility of…
Talk given at the Workshop on "Constraint Theory and Quantization Methods"; Montepulciano, Italy, June 1993 --- Instead of attempting to give a summary or to identify highlights of the workshop, the history of the development of analytical…
Topological defects are thought to be left behind by the cosmological phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory:…
In a circle (an S^1) with circumference 1 assume m objects distributed pseudo-randomly. In the universal covering R^1 assume the objects replicated accordingly, and take an interval L>1. In this interval, make the normalized histogram of…
I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…