Related papers: Knot Physics on Entangled Vortex-Membranes: Classi…
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to isometry) normal form at least when the…
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 statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter…
We study theoretically the dynamics of charged quantized vortices (CQVs). CQVs (ion-vortex complexes) have been used as an important probe in the field of quantum hydrodynamics. Recent experimental studies of quantum turbulence at very low…
Vortex stretching is a common feature of many complex flows, including turbulence. Experiments and simulations of isolated vortex knots demonstrate that this behavior can also be seen in relatively simple systems, and appears to be…
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
The structure of a vortex in the inner crust of neutron stars is calculated within the framework of quantum mean field theory taking into account the interaction with the nuclei composing the Coulomb lattice. Making use of the results…
We study binary Bose-Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. Within the mean-field theory, the two types of fields have been shown to give the same vortex-lattice phase…
We study the scattering of noncommutative vortices, based on the noncommutative field theory developed in [Phys. Rev. D 75, 045009 (2007)], as a way to understand the interaction of cosmic strings. In the center-of-mass frame, the effects…
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…
In this paper we constructed new model of plastic deformation. The knot theory was used to classify the plastic state.
A numerical simulation shows that the osmotic pressure of compressed lattice knots is a function of knot type, and so of entanglements. The osmotic pressure for the unknot goes through a negative minimum at low concentrations, but in the…
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…
A time crystal is a time dependent physical system that does not reach a standstill, even in state of minimum energy. Here we show that the stability of a time crystal can be enhanced by its topology. For this we simulate time crystals made…
Quantum Chromodynamics and Quantum Electrodynamics, both renormalizable quantum field theories with a small number of precisely constrained input parameters, dominate the dynamics of the quarks and gluons - the underlying building blocks of…
We propose two types of topologically stable knot solitons in condensed matters, one in two-component Bose-Einstein condensates and one in two-gap superconductors. We identify the knot in Bose-Einstein condensates as a twisted vorticity…
After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological…
In this thesis, we consider the dynamics of vortices in the easy plane insulating ferromagnet in two dimensions. In addition to the quasiparticle excitations, here spin waves or magnons, this magnetic system admits a family of vortex…
The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction…
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…