  Soft matter (e.g., biomaterials, polymers, sediments, oil, emulsions) has
become an important bridge between physics and diverse disciplines. Its
fundamental physical mechanism, however, is largely obscure. This study made
the first attempt to connect fractional Schrodinger equation and soft matter
physics under a consistent framework from empirical power scaling to
phenomenological kinetics and macromechanics to mesoscopic quantum mechanics.
The original contributions are the fractional quantum relationships, which show
Levy statistics and fractional Brownian motion are essentially related to
momentum and energy, respectively. The fractional quantum underlies fractal
mesostructures and many-body interactions of macromolecules in soft matter and
is experimentally testable.
