Abstract
The flux averaged Kubo-Hall conductivity σ̄ (which is related to Berry's phase associated with the adiabatic ground state) is not a topological invariant (contrary to previous claims), since the parameter space is not a torus due to the general form of the flux dependence of adiabatic wave functions in the presence of disorder. Therefore σ̄ seems inadequate for a description of the integer quantum Hall conductance. This is consistent with recent results on systems with periodic boundary conditions, which show that the macroscopic Hall current originates from the nonadiabatic states and that an important part of the microscopic particle dynamics in the quantum Hall regime cannot be described by linear response theory.
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