  We study fluctuations of the matrix coefficients for the quantized cat map.
We consider the sum of matrix coefficients corresponding to eigenstates whose
eigenphases lie in a randomly chosen window, assuming that the length of the
window shrinks with Planck's constant. We show that if the length of the window
is smaller than the square root of Planck's constant, but larger than the
separation between distinct eigenphases, then the variance of this sum is
proportional to the length of the window, with a proportionality constant which
coincides with the variance of the individual matrix elements corresponding to
Hecke eigenfunctions.
