An approach to Quantum Hall Effect

The phonon exchange between the electron and the elementary magnetic flux (fluxon, half-spin fermion) binds an electron-fluxon composite. The center-of-mass of the composite moves as a boson with the linear dispersion relation: epsilon = (2/pi)nu(F)q, nu(F) = Fermi speed. The 2D system of free composite bosons undergoes a Bose-Einstein condensation at k(B)T(c) = 1.24 hnu(F)n(0)(1/2), where n(0) is the density. The plateau value (Q/P)(h/e(2)) at the fractional Landau-level occupation ratio v = P/Q, odd Q, directly indicates the fractional charge (magnitude) e/Q for the composite with Q fluxons.