  We have considered heat conduction in a one-dimensional mass disordered
harmonic chain of $N$ particles connected to two Langevin type reservoirs at
different temperatures. An exact expression for the boundary heat
current-current auto-correlation function in the non-equilibrium steady state
(NESS) is obtained in terms of non-equilibrium phonon Green's functions. The
time integral of the correlation function gives expected result, both in
non-equilibrium as well as equilibrium cases. Using the form of this
correlation function we show that asymptotic system size dependence of current
fluctuation in NESS for a mass disordered harmonic chain is $N^{-\alpha}$ for
different boundary conditions. For free and fixed boundary conditions we get
$\alpha=1/2$ and 3/2 respectively, while for pinned case the fluctuation decays
exponentially with system size.
