Related papers: Knots in interaction
Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if…
A {\it stuck knot} is a knot diagram containing designated crossings, called {\it stuck crossings}, whose incident strands are required to remain locally non-separable. These rigidity constraints restrict the allowable ambient isotopies and…
The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular…
Coherent coupling of two qubits mediated by a nonlinear resonator is studied. It is shown that the amount of entanglement accessible in the evolution depends both on the strength of nonlinearity in the Hamiltonian of the resonator and on…
An oriented compact 4-manifold $V$ with boundary $S^3$ is called a positon (resp. negaton) if its intersection form is positive definite (resp. negative definite) and it is simply connected. In this paper, we prove that there exist…
Generation, interaction and detection of dark solitons in Bose-Einstein condensates is considered. In particular, we focus on the dynamics resulting from phase imprinting and density engineering. The generation of soliton pairs as well as…
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal…
We predict solitary vortices in quasi-planar condensates of dipolar atoms, polarized parallel to the confinement direction, with the effective sign of the dipole-dipole interaction inverted by means of a rapidly rotating field. Energy…
The nature of the interaction of a soliton with an attractive well is elucidated using a model of two interacting point particles. The system shows the existence of trapped states at positive kinetic energy, as well as reflection by an…
The resonant interaction between two two-level atoms and m- electromagnetic modes in a cavity is considered. Entanglement dynamics between two atoms is examined. In particular we compare dynamical variations for different cavity modes as…
We study two-dimensional (2D) solitons in the mean-field models of ultracold gases with long-range quadrupole-quadrupole interaction (QQI) between particles. The condensate is loaded into a deep optical-lattice (OL) potential, therefore the…
The mechanical properties of polymer knots under stretching in a bad or good solvent are investigated by applying a given force $F$ to a point of the knot while keeping another point fixed. The Monte Carlo sampling of the polymer…
We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected,…
The proton is a composite object with spin one-half, understood to contain highly relativistic spin one-half quarks exchanging spin-one gluons, each possibly with significant orbital angular momenta. While their fundamental interactions are…
Quantum vortices play an important role in the physics of two-dimensional quantum many-body systems, though they usually are understood in the single-particle framework like the mean-field approach. Inspired by the study on the relations…
We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states.…
A long-range soliton interaction is discussed whereby two or more dark solitons interact in an inhomogeneous atomic condensate, modifying their respective dynamics via the exchange of sound waves without ever coming into direct contact. An…
Interference patterns associated with soliton-soliton interaction are investigated in detail. We find that the temporal and spatial interference patterns exhibit quite different characteristics. The period of the spatial interference…
We present a method for numerically building a vortex knot state in the superfluid wave-function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and stability of the two…
The vortex patterns stabilized by the square array of artificial pinning sites with a tunable pinning strength are studied by using a phenomenological approach in the London limit. The transitions between pinned and deformed triangular…