Related papers: When do knots in light stay knotted?
Given a grid diagram for a knot or link K in $S^3$, we construct a filtered spectrum whose homology is the knot Floer homology of K. We conjecture that the filtered homotopy type of the spectrum is an invariant of K. Our construction does…
Inspired by the issue of stability of molecular structures, we investigate the strict minimality of point sets with respect to configurational energies featuring two- and three-body contributions. Our main focus is on characterizing those…
We investigate the trajectories of point charges in the background of finite-action vacuum solutions of Maxwell's equations known as knot solutions. More specifically, we work with a basis of electromagnetic knots generated by the so-called…
The existence of the zero point electromagnetic field in the dark is a trivial property of classical electromagnetism. Splitting the total, genuine electromagnetic field into the sum of a conventional field and a zero point field is…
Most of the enveloppes of Planetary Nebulae (and other objects like novae) are far from beeing homogeneous: clumps, knots and tails are often observed. We present here the first attempt to build a 3D-photoionization model of a knot and the…
An atom that couples to two distinct leaky optical cavities is driven by an external optical white noise field. We describe how entanglement between the light fields sustained by two optical cavities arises in such a situation. The…
Among the possibly most intriguing aspects of quantum entanglement is that it comes in "free" and "bound" instances. Bound entangled states require entangled states in preparation but, once realized, no free entanglement and therefore no…
It is demonstrated that the strong coupling of an electron gas to photons in systems with broken time-reversal symmetry results in bound electron-photon states which cannot be backscattered elastically. As a consequence, the electron gas…
The aim of this paper is to investigate the properties of magnetic reconnection at a 3D null point, with respect to their dependence on the symmetry of the magnetic field around the null. In particular we examine the rate of flux transport…
We consider the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain or at a straight line. We give a criterion on initial curves that guarantees the appearance of a singularity in finite…
This paper applies the notion of relative CR embeddings to study two related questions. First, it answers negatively the question posed by Penrose whether every shear-free null rotating congruence is analytic. Second, it proves that given…
The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.
The concept of a noncommutative field is formulated based on the interplay between twisted Poincar\'e symmetry and residual symmetry of the Lorentz group. Various general dynamical results supporting this construction, such as the…
A Heisenberg uncertainty relation is derived for spatially-gated electric and magnetic field fluctuations. The uncertainty increases for small gating sizes which implies that in confined spaces the quantum nature of the electromagnetic…
Within the first quantisation of Maxwell's equations, we introduce the dynamic energy, linear momentum, angular momentum and optical spin of the electromagnetic fields. We show that these different quantities are conserved during the…
I conjecture that only those states of light whose Wigner function is positive are real states, and give arguments suggesting that this is not a serious restriction. Hence it follows that the Wigner formalism in quantum optics is capable of…
Solutions of the Maxwell equations for electrostatic systems at rest on the rotating Earth's surface are shown to exhibit a nonvanishing magnetic field despite zero electric currents in the system. Such a field is of pure geometric origin,…
It is a consequence of theorems of Gordon-Reid [Tangle decompositions of tunnel number one knots and links, J. Knot Theory and its Ramifications, 4 (1995) 389-409] and Thompson [Thin position and bridge number for knots in the 3-sphere,…
Consider a continuous flow in $\mathbb{R}^3$ or any orientable $3$-manifold. Let $(Q_1, Q_0)$ be an index pair in the sense of Conley and consider the region $N := \overline{Q_1 - Q_0}$. (An example of this is a compact $3$-manifold $N$…
Magnetic nulls are locations where the magnetic field vanishes. Nulls are the location of magnetic reconnection, and they determine to a large degree the magnetic connectivity in a system. We describe a novel approach to understanding…