Related papers: A problem of Ulam about magnetic fields generated …
A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities…
We demonstrate guiding of cold neutral atoms along a current carrying wire. Atoms either move in Kepler-like orbits around the wire or are guided in a potential tube on the side of the wire which is created by applying an additional…
In an earlier paper we introduced rectangular diagrams of surfaces and showed that any isotopy class of a surface in the three-sphere can be presented by a rectangular diagram. Here we study transformations of those diagrams and introduce…
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…
Historically originated as a sub-field of topology, knot theory is an active area of mathematical investigation that has strong connections with a diverse set of scientific fields such as algebra, biology, and statistical mechanics. A…
By a fixed continuous map from a $3$-space to itself, a knot in the $3$-space may be mapped to another knot in the $3$-space. We analyze possible knot types of them. Then we map a knot repeatedly by a fixed continuous map and analyze…
We prove that each overtwisted contact structure has knot types that are represented by infinitely many distinct transverse knots all with the same self-linking number. In some cases, we can even classify all such knots. We also show…
An intersecting D3-D3' system contains magnetic monopole solutions due to D- strings stretched between two branes. These magnetic charges satisfy the usual Dirac quantization relation. We show that this quantization condition can also be…
In this Letter we reanalyse the question of the origin of magnetic fields during the electroweak phase transition. We show that their formation is intimately connected to some semiclassical configurations of the gauge fields, such as…
We have studied the force in mesoscopic wires in the presence of an external magnetic field along the wire using a free electron model. We show that the applied magnetic field can be used to affect the force in the wire. The magnetic field…
Based on the quantum two-body problem introduced in [arXiv:1604.06693] we consider bound pairs of electrons moving on the positive half-line. The analysis is motivated by the ground-breaking work of Cooper who identified the pairing of…
(NOTE: per referee comments, this article has been split; it is now superseded by "Existence of thread-wire minimizers" and "Near-wire thread-wire minimizers"; please see http://www.bkstephens.net.) Alt's thread problem asks for least-area…
Cosmic strings are topological defects which can be formed as a result of phase transitions with a spontaneous symmetry breaking in the early Universe. The possibility of the generation of a magnetic field around a cosmic string on the…
Here we consider an interplay between the topology of the magnetization texture (which is a topological soliton, or Skyrmion) in a planar magnetic nano-element and the topology of the element itself (its connectivity). We establish the…
A magnetic Skyrmion is a stable two-dimensional nanoparticle describing a localized winding of the magnetization in certain magnetic materials. Skyrmions are the subject of intense experimental and theoretical investigation and have…
Ballistic quantum wires are exposed to longitudinal profiles of perpendicular magnetic fields composed of a spike (magnetic barrier) and a homogeneous part. An asymmetric magnetoconductance peak as a function of the homogeneous magnetic…
We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative…
We present the formalism for the covariant treatment of gravitational radiation in a magnetized environment and discuss the implications of the field for gravity waves in the cosmological context. Our geometrical approach brings to the fore…
We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple…
Magnetic monopoles have been a subject of interest since Dirac established the relation between the existence of a monopole and charge quantization. 't Hooft and Polyakov proved that they can arise from gauge theories as the result of a non…