The Cantorian structure of the background magnetic field and high temperature superconductors

One builds the solution of GL equation in terms of the elliptic cn function of complex argument. The real part of the complex action, (S) under bar = (h) over bar ln cn(u), corresponds to the potential of a vortex lattice, an d from here, through the elliptic function degeneration, to the vortex stre ets. Considering the vortex streets fixed on vacuum by a background magneti c held through pinning, from equating the current density to zero one deter mines the field structure: the mean value will be roughly equal to Bo, and its flux will be fractional. The fractional flux will be associated to quas i-particles obeying the 'anyonic' statistics. At low temperatures and high external magnetic field, the structure of background field will be of Canto rian type. (C) 2000 Elsevier Science Ltd. All rights reserved.