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

Generalized self-consistent reservoir model for normal and anomalous heat transport in quantum harmonic chains.

Fictitious stochastic reservoirs incorporate scattering and dephasing mechanisms into the system in contact with these reservoirs. The reservoir-system coupling is described by the related self-energy in terms of the nonequilibrium Green's function formalism or equivalently the quantum Langevin equation formalism. In this study, we investigate thermal transport in a finite segment of an infinitely extended quantum harmonic chain with an equal self-energy at each site by using the self-consistent reservoir approach. In this setup, the entire system is lattice translation invariant so that mismatched boundaries are excluded from the model. Solving the Landauer-Büttiker equations under the self-consistent adiabatic condition, we quantitatively elucidate a thermally induced crossover of ballistic-to-diffusive transport and its scaling relation prescribed by a temperature-dependent mean free path. It is also shown that normal transport emerges in the diffusive limit for a linear self-energy, while nonlinear higher-order ones generically lead to anomalous transport. Physical implications of these observations are discussed in terms of the persistence of a massless Goldstone mode as well as the conservation of total linear momentum.