Related papers: Topological Interplay between Knots and Entangled …
When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological…
Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil…
Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here, we find…
The entanglement of open curves in 3-space appears in many physical systems and affects their material properties and function. A new framework in knot theory was introduced recently, that enables to characterize the complexity of…
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…
We study the mechanical buckling of a two dimensional membrane coated with a thin layer of superfluid. It is seen that a singularity (vortex or anti-vortex defect) in the phase of the quantum order parameter, distorts the membrane metric…
Coherence vortices are screw-type topological defects in the phase of Glauber's two-point degree of quantum coherence, associated with pairs of spatial points at which an ensemble-averaged stochastic quantum field is uncorrelated. Coherence…
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…
Three-dimensional three-colour percolation on a lattice made of tetrahedra is a direct generalization of two-dimensional two-colour percolation on the triangular lattice. The interfaces between one-colour clusters are made of bicolour…
We investigate the interaction of magnetic vortices and skyrmions with a spin-polarized current. In a square lattice, fixed classical spins and quantum itinerant electrons, evolve according to the coupled Landau-Lifshitz and Schr\"odinger…
The recently conjectured knots-quivers correspondence relates gauge theoretic invariants of a knot $K$ in the 3-sphere to representation theory of a quiver $Q_{K}$ associated to the knot. In this paper we provide geometric and physical…
We extend the entanglement bootstrap approach to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions, we define a…
We study pinning and unpinning of superfluid vortices in the inner crust of a neutron star using 3-dimensional dynamical simulations. Strong pinning occurs for certain lattice orientations of an idealized, body-centered cubic lattice, and…
Using a variational ansatz for the wave function of the Bose-Einstein condensate, we develop a quantum theory of vortices and quadrupole modes in a one-dimensional optical lattice. We study the coupling between the quadrupole modes and…
We prove the existence of knotted and linked thin vortex tubes for steady solutions to the incompressible Euler equation in R^3. More precisely, given a finite collection of (possibly linked and knotted) disjoint thin tubes in R^3, we show…
Interactions and reconnections of vortices are fundamental in many areas of physics, including classical and quantum fluids where they are central to understanding phenomena such as turbulence. In three-dimensional (3D) superfluids, quantum…
We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred…
In this paper we show how to place Michael Berry's discovery of knotted zeros in the quantum states of hydrogen in the context of general knot theory and in the context of our formulations for quantum knots. Berry gave a time independent…
We present a new paradigm for three dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension three is the existence of singularities. We show how to use knot…
We discuss a new type of topological defect in XY systems where the O(2) symmetry is broken in the presence of a boundary. Of particular interest is the appearance of such defects in nanomagnets with a planar geometry. They are manifested…