Fluxals

Fluxals are a theoretical construct used in physics and information theory to describe discrete, quantized units of flux that can move through a medium or network. They generalize the notion of magnetic flux and topological charge by treating flux as a mobile, particle-like excitation whose presence is detected by a fluxal number associated with a region.

In mathematical terms, a fluxal is associated with a localized flux density F defined on a manifold or lattice. For a closed surface S surrounding a fluxal, the fluxal number φ is given by φ = ∮_S F · dS. Fluxals are typically quantized, taking values in a discrete set, and they obey conservation laws under allowed deformations of the system. In lattice models, fluxals are often tied to plaquette variables and act as sources or sinks of flux.

Interactions: Fluxals can be created or annihilated in combinations that conserve the total fluxal number modulo a symmetry. When two fluxals are braided or interchanged, the system can acquire a phase or undergo a fusion that changes the net fluxal content, a feature analogous to anyons in two-dimensional systems.

Realizations and applications: Fluxals appear as emergent excitations in certain spin liquids, superconducting circuits, and photonic lattices. They provide a framework for modeling robust information transfer and topologically protected states, with potential implications for quantum computation and network design.

See also: magnetic flux, topological defect, anyon, soliton, lattice gauge theory, spin liquid.