Controlling the size scaling of the thermal conductivity in harmonic chains with correlated mass disorder

We address the general problem of heat conduction in one dimensional harmonic chains, with correlated isotopic disorder, attached at their ends to white noise or Rubin's model of heat baths. The scaling behavior of the thermal conductivity is independent of the heat reservoirs, but depends on the boundary conditions and the low wave-number μ behavior of the power spectrum W(μ) of the fluctuations of the random masses around their common mean value. Thus, by properly tuning W(μ) we are able to control the scaling of the thermal conductivity κ with the system size N. As an example, we show that if W(μ)∼exp⁡(−1/μ)/μ2, then κ∼N/(log⁡N)3 for fixed boundary conditions and κ∼N/log⁡(N) for free boundary conditions, which represent non-standard scalings of the thermal conductivity. In addition, we obtain the asymptotic dependence of the thermal conductivity on the coupling strength between the harmonic chain and the heat baths. •We study the heat conduction in one dimensional harmonic chains with correlated isotopic disorder.•We discuss the conditions for non-standard scalings of the thermal conductivity with the system size.•We show that the asymptotic thermal conductivity does not depend on the spectral properties of the thermal baths.