In a disordered mesoscopic system, the typical spacing between the peaks and
the valleys of the conductance as a function of Fermi energy EF is called
the conductance energy correlation range Ec. Under the ergodic hypothesis,
the latter is determined by the half-width of the ensemble averaged conductance
correlation function: F=. In
ordinary diffusive metals, Ec∼D/L2, where D is the diffusion constant
and L is the linear dimension of the phase-coherent sample. However, near a
quantum phase transition driven by the location of the Fermi energy EF, the
above picture breaks down. As an example of the latter, we study, for the first
time, the conductance correlations near the integer quantum Hall transitions of
which EF is a critical coupling constant. We point out that the behavior of
F is determined by the interplay between the static and the dynamic
properties of the critical phenomena.Comment: 4 pages, 4 figures, minor corrections, to appear in Phys. Rev. Let