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 precise 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. The 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 results are valid for a fractional plateau near the filling factor p/q if charge e is replaced by e/q.