Propriedades do transporte de calor em cristais harmônicos e anarmônicos com massas alternadas.

Abstract

We analytically investigate the heat transport in a few one-dimensional crystals with alternate masses, whose ends are connected to thermal reservoirs at unequal temperatures. We consider both the quantum and classical versions of the harmonic model, for which the Fourier law does not hold, as well as a classical chain of oscillators with self-consistent reservoirs connected to the inner sites and subject to an anharmonic on-site potential, in which case the Fourier law does hold. For the harmonic model in the classical high temperature regime, we rigorouslycalculate the exact expression of the heat current, thus extending previous results in the literature. We show that a thermal insulating effect emerges in a chain with alternate large and small masses as compared to a homogeneous chain with large masses, the effect being considerably more pronounced in the absence of the on-site potential.We also analyze the harmonic model in the linear-response, low-temperature regime, for which the quantum mechanical effects become important. In the latter case, we obtain estimates for the heat current in both the homogeneous large-mass chain and the one with alternate large and small masses, thus showing that the insulating effectobserved in the classical limit still holds in the low-temperature regime.Finally, we follow a non-rigorous approach in order to study the heat transport in a classical nonlinear model with self-consistent reservoirs connected to the inner sites. We obtain approximate expressions for both the heat current and the temperature profile in the non-equilibrium stationary state. We then show that an insulating effect similar to the one observed in the harmonic model with anomalous thermal conductivity also holds for this nonlinear classical model with normal conductivity.A similar effect holds if the on-site potentials are alternated, instead of the particle masses. The existence of such insulating effect in models as different to one another as the ones we analyze indicates that it may be a general property of one-dimensional systems with alternate masses, with possible applications in the heat-flow control.