Related papers: Tight composites knots and chirality
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…
Chirality plays a major role in nature, from particle physics to DNA, and its control is much sought-after due to the scientific and technological opportunities it unlocks. For magnetic materials, chiral interactions between spins promote…
The concept of chirality makes ubiquitous appearance in nature. Particularly, both a structure and its collective excitations may acquire well defined chiralities. In this work, we reveal an intrinsic connection between the chiralities of a…
The different quantum phases appearing in strongly correlated systems as well as their transitions are closely related to the entanglement shared between their constituents. In 1D systems, it is well established that the entanglement…
The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the…
The homology and cohomology of quandles and racks are used in knot theory: given a finite quandle and a cocycle, we can construct a knot invariant. This is a quick introductory survey to the invariants of knots derived from quandles and…
Microscopic origin of chirality and possible electric-field induced rotation and rotation-field induced electric polarization are investigated. By building up a realistic tight-binding model for elemental Te crystal in terms of…
Electrons which are slowly moving through chiral magnetic textures can effectively be described as if they where influenced by electromagnetic fields emerging from the real-space topology. This adiabatic viewpoint has been very successful…
Inspired by recent developments in electron chirality, we reconsider some microscopic physical quantities that have been overlooked or have received little attention in condensed matter physics, based on the non-relativistic limit of the…
Though extensively studied, hardness, defined as the resistance of a material to deformation, still remains a challenging issue for a formal theoretical description due to its inherent mechanical complexity. The widely applied Teter's…
Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An…
Magnetic and chiral bands have been a hot subject for more than twenty years. Therefore, quite large volumes of experimental data as well as theoretical descriptions have been accumulated. Although some of the formalisms are not so easy to…
Chirality induced by rolling a two-dimensional material into a spiral geometry reshapes its electronic band structure. In this work, we theoretically investigate the topological properties of carbon nanoscrolls under an axial magnetic…
In this paper, we introduce the notion of strong geometry, a structure composed by both the chirotope of a set of points X in the d-dimensional space and the wedge chirotope which is the specific adjoint chirotope induced by the hyperplanes…
We consider spinorial fields in polar form to deduce their respective tensorial connection in various physical situations: we show that in some cases the tensorial connection is a useful tool, instead in other cases it arises as a necessary…
The viscous flow of polymer chains in dense melts is dominated by topological constraints whenever the single chain contour length, N, becomes larger than the characteristic scale Ne, defining comprehensively the macroscopic rheological…
Chiroptical effects, characterized by different optical responses for left- (LCP) and right- handed circularly polarized light (RCP), are powerful and valuable tools in optics with wide applications in polarization resolved imaging and…
Chirality is a universal feature in nature, as observed in fermion interactions and DNA helicity. Much attention has been given to chiral interactions of light, not only regarding its physical interpretation but also focusing on intriguing…
We develop a family of chiral measures to quantify the chirality of a distribution and assign it a handedness. Our measures are built using the tensorial moments of the distribution, which naturally encode its spatial character, not only…