Dimensional crossover of thermal transport in quantum harmonic lattices coupled to self-consistent reservoirs

In this study, we investigate thermal transport in d-dimensional quantum harmonic lattices coupled to self-consistent reservoirs. The d-dimensional system is treated as a set of Klein-Gordon chains by exploiting an orthogonal transformation. For generality, the self-energy that describes the reservoir-system coupling is assumed to be a power function of energy Σ∝-iɛ^{n}, where n is limited to odd integers because of the reality condition. Total momentum conservation is violated for n=1 but otherwise preserved. In this approach, we show that for n=1, thermal conductivity remains finite in the thermodynamic limit and normal transport takes place for an arbitrary value of d. For n=3,5,7,⋯, however, thermal conductivity diverges and thermal transport becomes anomalous as long as d