Cyclic Statistics In Three Dimensions
نویسنده
چکیده
While 2-dimensional quantum systems are known to exhibit non-permutation, braid group statistics, it is widely expected that quantum statistics in 3-dimensions is solely determined by representations of the permutation group. This expectation is false for certain 3-dimensional systems, as was shown by the authors of [1, 2, 3]. In this work we demonstrate the existence of “cyclic”, or Zn, non-permutation group statistics for a system of n > 2 identical, unknotted rings embedded in R. We make crucial use of a theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch relations for the automorphisms of the free product group on n elements.
منابع مشابه
On the effect of grain size on rock behavior under cyclic loading by distinct element method
It is well-known that the mechanical behavior of rocks under cyclic loading is much different from static loading conditions. In most constructions, the load applied to structures is within dynamic ranges. That’s why a great deal of attention has been paid towards this field in order to identify the dynamic behavior of rocks in more details. Nevertheless, the nature of dynamic failure in rocks ...
متن کاملA unified theoretical harmonic analysis approach to the cyclic wavelet transform (CWT) for periodic signals of prime dimensions
The article introduces cyclic dilation groups and finite affine groups for prime integers, and as an application of this theory it presents a unified group theoretical approach for the cyclic wavelet transform (CWT) of prime dimensional periodic signals.
متن کاملFixed point theory for cyclic $varphi$-contractions in fuzzy metric spaces
In this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. Meantime, an example is provided toillustrate this theorem. The main result shows that a self-mappingon a G-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. Afterwards, some results inco...
متن کاملCyclic Cellular Automata in 3D
Cyclic cellular automata in two dimensions have long been intriguing because they self organize into spirals and that behavior can be analyzed. The form for the patterns that develop is highly dependent upon the form of the neighborhood. We extend this work to three dimensional cyclic cellular automata and observe self organization dependent upon the neighborhood type. This includes neighborhoo...
متن کاملComparison of Radial Consolidation Behavior of Clay under Three Types of Cyclic Loading
Vertical drains and stone columns which have been used in infrastructure construction for highways, ports, coastal regions, etc., provide significant benefits for improving soil characteristics such as reducing the drainage length and accelerating the consolidation process. So the investigation of the radial consolidation is inevitable. Soils may be subjected to cyclic loading such as silos, ta...
متن کامل