  We consider heat transport in one-dimensional harmonic chains with isotopic
disorder, focussing our attention mainly on how disorder correlations affect
heat conduction. Our approach reveals that long-range correlations can change
the number of low-frequency extended states. As a result, with a proper choice
of correlations one can control how the conductivity $\kappa$ scales with the
chain length $N$. We present a detailed analysis of the role of specific
long-range correlations for which a size-independent conductivity is exactly
recovered in the case of fixed boundary conditions. As for free boundary
conditions, we show that disorder correlations can lead to a conductivity
scaling as $\kappa \sim N^{\varepsilon}$, with the scaling exponent
$\varepsilon$ being arbitrarily small (although not strictly zero), so that
normal conduction is almost recovered even in this case.

Disordered Systems and Neural Networks;Statistical Mechanics