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We address the general problem of heat conduction in one dimensional harmonic chain, with correlated isotopic disorder, attached at its ends to white noise or oscillator heat baths. When the low wavelength $mu$ behavior of the power spectrum $W$ (of the fluctuations of the random masses around their common mean value) scales as $W(mu)sim mu^beta$, the asymptotic thermal conductivity $kappa$ scales with the system size $N$ as $kappa sim N^{(1+beta)/(2+beta)}$ for free boundary conditions, whereas for fixed boundary conditions $kappa sim N^{(beta-1)/(2+beta)}$; where $beta>-1$, which is the usual power law scaling for one dimensional systems. Nevertheless, if $W$ does not scale as a power law in the low wavelength limit, the thermal conductivity may not scale in its usual form $kappasim N^{alpha}$, where the value of $alpha$ depends on the particular one dimensional model. As an example of the latter statement, if $W(mu)sim exp(-1/mu)/mu^2$, $kappa sim N/(log N)^3$ for fixed boundary conditions and $kappa sim N/log(N)$ for free boundary conditions, which represent non-standard scalings of the thermal conductivity.
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-f
We consider heat transport in one-dimensional harmonic chains attached at its ends to Langevin heat baths. The harmonic chain has mass impurities where the separation $d$ between any two successive impurities is randomly distributed according to a po
We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{alpha}$, where $k$ is the wave-vector of the modulations on the random masses landscape.
We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as $sim r^{-a}$. Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical p
We use large-scale Monte Carlo simulations to test the Weinrib-Halperin criterion that predicts new universality classes in the presence of sufficiently slowly decaying power-law-correlated quenched disorder. While new universality classes are reason