相关论文: Note on the 8$_{18}$-Knot

We illustrate schematically a possible traversing along the path of trefoil-type and $8_{18}$ knots during a specific time period by considering a quantum-mechanic system which satisfies a specific kind of phase dynamics of quantum…

This an article about some elementary geometric and combinatorial natures of various knot energies. A related "new" knot invariant -- the X-crossing number -- is introduced.

We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved…

It has been suggested recently that knots might exist as stable soliton solutions in a simple three-dimensional classical field theory, opening up a wide range of possible applications in physics and beyond. We have re-examined and extended…

Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can…

I consider the quantum interference of electrons moving along knotted trajectories under external magnetic field. The induced persistent current is formulated in terms of characteristic parameters that classify the torus knot geometry. The…

This document provides detailed descriptions of data acquisition and data analysis in support of the accompanying Article, cond-mat/0610721: Observation of the two-channel Kondo effect. Some of the most intriguing problems in solid state…

Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and…

We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented.…

In this note, I describe a formalism for treating knots as geometric spaces, and make an application to a simple statistical mechanics computation. The motivation for this study is the natural visual symmetry of the knot, and I describe how…

Near the sample edge, or a sharp magnetic field step the drift of two-dimensional electrons in a magnetic field has the form of skipping/snake orbits. We show that families of skipping/snake orbits of electrons injected at one point inside…

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

The electronic structure of heavy elements, when described in a space-time which the metric is affected by the electromagnetic interaction, presents instabilities. These instabilities increase with the atomic number, and above a critical…

We establish a necessary and sufficient condition for a heptagonal knot to be figure-8 knot. The condition is described by a set of Radon partitions formed by vertices of the heptagon. In addition we relate this result to the number of…

The ratio of volume to crossing number of a hyperbolic knot is known to be bounded above by the volume of a regular ideal octahedron, and a similar bound is conjectured for the knot determinant per crossing. We investigate a natural…

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…

The choice that a solid system "makes" when adopting a crystal structure (stable or metastable) is ultimately governed by the interactions between electrons forming chemical bonds. By analyzing 6 prototypical binary transition-metal…

We study the geometry of interacting knotted solitons. The interaction is local and advances either as a three-body or as a four-body process, depending on the relative orientation and a degeneracy of the solitons involved. The splitting…

The ability to shuttle coherently individual electron spins in arrays of quantum dots is a key procedure for the development of scalable quantum information platforms. It allows the use of sparsely populated electron spin arrays, envisioned…

Knots across various length scales, from micro to macro-scales, such as polymers, DNA, shoelaces, and surgery, serving their unique mechanical properties. The shape of ideal knots has been extensively studied in the context of knot theory,…