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Phonon thermal conductivity by non-local non-equilibrium molecular dynamics

Non-equilibrium (NE) molecular dynamics (MD), or NEMD, gives a "direct" simulation of thermal conductivity kappa. Heat H(x) is added and subtracted in equal amounts at different places x. After steady state is achieved, the temperature T(x) is found by averaging over finite sections. Usually the aim is to extract a value of dT/dx from a place distant from sources and sinks of heat. This yields an effective kappa(L) for the thermal conductivity, L being the system size. The result is then studied as a function of L, to extract the bulk limit kappa. Here instead, our heat is H(x)~sin(qx), where q=2pi/L. This causes a steady-state temperature T_0 + Delta T sin(2pi x/L). A thermal conductivity kappa(q) is extracted, which is well converged at the chosen q (or L). Bulk conductivity kappa requires taking the q to 0 limit. The method is tested for liquid and crystalline argon. One advantage is reduced computational noise at a given total MD run time. Another advantage is that kappa(q) has a more physical meaning than kappa(L). It can be easily studied using Peierls-Boltzmann transport theory. New formulas for kappa(q) in simplified Debye-type models give new insight about extrapolation to q to 0 or 1/L to 0. In particular, it is shown that kappa(L$ is unlikely to behave as kappa -C/L, and much more likely to behave as kappa-C'/sqrt(L). Convergence problems encountered in computational cells with very large aspect ratios L(parallel)/L(perp) are also analyzed. Some details are contained in the "Supplemental Material" file.