Fractional calculus connects two- and one-dimensional phase behavior (IMAGE)
Caption
Schematic comparison of a conventional two-dimensional local model and a one-dimensional fractional nonlocal model.
The left-hand region represents a two-dimensional system described by first-order spatial derivatives, while the right-hand region represents a one-dimensional system described by a half-order derivative. Introducing the fractional derivative creates long-range spatial coupling in one dimension. The upper panel illustrates the more strongly correlated low-temperature state, and the lower panel illustrates the disordered high-temperature state. White circles mark vortices in the two-dimensional illustration. The one-dimensional model shows BKT-like correlation scaling, although a corresponding microscopic defect-unbinding mechanism has not been established.
Credit
Michikazu KOBAYASHI from kochi university of technology
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