ACTIVATED CONDUCTIVITY IN THE QUANTUM HALL-EFFECT

Activated dissipative conductivity sigma(xx) = sigma(xx) exp(-Delta/T ) and the activated deviation of the Hall conductivity from the precis e quantization delta sigma(xy) = sigma(xy) -ie(2)/h = sigma(xy) exp(- Delta/T) are studied in a plateau range of the quantum Hall effect. Th e prefactors sigma(xx) and sigma(xy)* are calculated for the case of a long-range random potential in the framework of a classical theory. There is a range of temperatures T-1 << T << T-2 where sigma(xx) = e( 2)/h. In this range sigma(xy) approximate to (e(2)/h)(T/T-2)(80/21) < < sigma(xx). At large T >> T-2, on the other hand, sigma(xy)* = e(2)/ h and sigma(xx) = (e(2)/h)(T-2/T)(10/13) << sigma(xy)*. Similar resul ts are valid for a fractional plateau near the filling factor p/q if c harge e is replaced by e/q.