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We show that the space of long knots in an euclidean space of dimension larger than three is a double loop space, proving a conjecture by Sinha. We construct also a double loop space structure on framed long knots, and show that the map…
A particular Riemannian metric which originally has been obtained for a well-known coordinate system in the Euclidean 3-space, is shown to specify, in fact, a manifold with boundary. There are two ways to make the manifold complete. One is…
A new concept for spinning unmagnetized plasma is demonstrated experimentally. Plasma is confined by an axisymmetric multi-cusp magnetic field and biased cathodes are used to drive currents and impart a torque in the magnetized edge.…
The origin of thermal and quantum entanglement in a class of three-dimensional spin models, at low momenta, is traced to purely topological reasons. The establishment of the result is facilitated by the gauge principle which, when used in…
We study the dynamics of entanglement in the one-dimensional spin-1/2 XY model in the presence of a transverse magnetic field. A pair of spins are considered as an open quantum system, while the rest of the chain plays the role of the…
In this paper, we study the entanglement entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on…
In a system where two identical two-level atoms interact with their common one-mode cavity field, it is shown that entanglement can become abruptly frozen in time, remaining at a constant value for a period of time until it begins to thaw…
Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…
Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in…
Einstein, Podolsky, and Rosen discussed their paradox in terms of measuring the positions or momenta of two particles. These degrees of freedom can become entangled upon scattering, but how much entanglement can be created in this process?…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
In mathematics, a knot is a single strand of string crossed over itself any number of times, and connected at the ends. The Reidemeister Moves have been proven to be the three core moves necessary to fully untangle a knot. Some knots can be…
Entanglement entropy is crucial for understanding the link between quantum mechanics and information theory. This thesis investigates how energy fluctuations and acceleration affect entanglement entropy through three key scenarios. First,…
We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of…
This letter details a simple scheme to entangle two neutrons by successive scattering from a macroscopic sample. In zero magnetic field the entanglement falls as the sample size increases. However, by applying a field and tuning the…
Considering two-dimensional electron gases under a perpendicular magnetic field, we pinpoint a specific kind of long-range bipartite entanglement of the electronic motions. This entanglement is achieved through the introduction of bicomplex…
We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can…
Cables are ubiquitous in many settings and it is often useful to untangle them. However, cables are prone to self-occlusions and knots, making them difficult to perceive and manipulate. The challenge increases with cable length: long cables…
Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics…
This paper explores the connections between particle scattering and quantum information theory in the context of the non-relativistic, elastic scattering of two spin-1/2 particles. An untangled, pure, two-particle in-state is evolved by an…