Quantum heat transfer in harmonic chains with self-consistent reservoirs: Exact numerical simulations

Abstract

We describe a numerical scheme for exactly simulating the heat current behavior in a quantum harmonic chain with self-consistent reservoirs. Numerically-exact results are compared to classical simulations and to the quantum behavior under the linear response approximation. In the classical limit or for small temperature biases our results coincide with previous calculations. At large bias and for low temperatures the quantum dynamics of the system fundamentally differs from the closeto-equilibrium behavior, revealing in particular the effect of thermal rectification for asymmetric chains. Since this effect is absent in the classical analog of our model, we conclude that in the quantum model studied here thermal rectification is a purely quantum phenomenon, rooted in the quantum statistics.

Energy rectification in quantum graded spin chains: Analysis of the XXZ model

“…It is important to mention that the study of small systems, minimalistic mathematical prototypes or toy models may provide key information in physics. In a similar context, we recall, for example, that the existence of thermal rectification in the quantum graded chain of harmonic oscillators with inner baths (in contrast with absence in the classical model) has been first discovered in a chain with 3 sites only [10], and then confirmed in larger chains by means of numerical computations in a further work [11].…”

“…Consequently, this scarcity of quantum results, the present ambient of device miniaturization, together with the possibility of effects of quantum nature, makes the detailed study of energy transport in genuine quantum models a program of great importance. As an example of change in the transport properties due to the quantum/classical nature of the model, we recall that thermal rectification has been observed in the quantum graded harmonic chain of oscillators with inner baths [10,11], but it is absent in the classical version of the same model [12]. A natural candidate for a quantum model describing these transport phenomena would be the quantum version of the chain of anharmonic oscillators, but even its classical version is already a problem of extreme difficulty [13].…”

From Thermal Rectifiers to Thermoelectric Devices

“…The advantage of such ap-proach lies in its simplicity and independence from microscopic details of inelastic processes. Probe terminals have been widely used in the literature and proved to be useful to unveil nontrivial aspects of phase-breaking processes [49], heat transport and rectification [22,23,118,52,24,112,13,120], and thermoelectric transport [73,57,56,75,76,124,126,135,136,122,67,15,11,27,25]. The approach can be generalized to any number n p of probe reservoirs.…”

Inelastic effects in molecular transport junctions: The probe technique at high bias

“…44 , and simulations demonstrating nonlinear charge and energy functionality with a facile convergence were reported in Refs. 26,[45][46][47][48][49] . While the LBP method is gaining recognition in molecular electronic applications, the serious fundamental and operational differences between dephasing and voltage probes, in high bias applications, are generally not recognized.…”