Related papers: Knotting and higher order linking in physical syst…
Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena…
In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected subspace.
In a recent work [S. Asthana. New Journal of Physics 24.5 (2022): 053026], we have shown the interrelation of different nonclassical correlations in multiqubit systems with quantum coherence in a single logical qubit. In this work, we…
We study the behaviour of a nonrelativistic quantum particle interacting with different potentials in the spacetimes of topological defects. We find the energy spectra and show how they differ from their free-space values.
In this work, we theoretically study the quantum correlations present in an optomechanical system by invoking an additional cross-Kerr coupling between the optical and mechanical mode. Under experimentally achievable conditions, we first…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction of an actual physical quantum system.…
The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the…
We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be…
Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via…
We discuss possible relationships between geometric and topological interactions on one side and physical interactions on the other side.
Topological ordered states are exotic quantum states of matter that defy the usual description in terms of symmetry breaking and local order parameters. The type or order they feature is of non-local, topological nature, and it allows such…
The essence of the famed long-range entanglement as revealed in topologically ordered state is the paradoxical coexistence of short-range correlation and nonlocal information that cannot be removed through constant-depth local quantum…
Relative self-linking and linking "numbers" for pairs of knots in oriented 3-manifolds are defined in terms of intersection invariants of immersed surfaces in 4-manifolds. The resulting concordance invariants generalize the usual…
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…
Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
We study the quantum correlations in a 2D system that possesses a topological quantum phase transition. The quantumness of two-body correlations is measured by quantum discord. We calculate both the correlation of two local spins and that…
It has been demonstrated both theoretically and experimentally that genuine multipartite entanglement between qubits can exist even in the absence of multipartite correlations. Here we provide first examples of this effect in higher…
In this paper, after some recalls about connectivity structures and about the formalisms of quantum mechanics, we associate some families of connectivity structures with any entangled quantum state, and with any "measurement device" on such…