Scaling analysis of negative differential thermal resistance

Abstract

Negative differential thermal resistance (NDTR) can be generated for any one-dimensional heat flow with a temperature-dependent thermal conductivity. In a system-independent scaling analysis, the general condition for the occurrence of NDTR is found to be an inequality with three scaling exponents: $n_1{n}_2<-(1+n_3)$, where $n_1\in (-\infty ,+\infty )$ describes a particular way of varying the temperature difference, and $n_2$ and $n_3$ describe, respectively, the dependence of the thermal conductivity on an average temperature and on the temperature difference. For cases with a temperature-dependent thermal conductivity, i.e. $n_2\ne 0$, NDTR can \emph{always} be generated with a suitable choice of $n_1$ such that this inequality is satisfied. The results explain the illusory absence of a NDTR regime in certain lattices and predict new ways of generating NDTR, where such predictions have been verified numerically. The analysis will provide insights for a designing of thermal devices, and for a manipulation of heat flow in experimental systems, such as nanotubes.

To be published in Physical Review E

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• Strong system-bath coupling induces negative differential thermal conductance and heat amplification in nonequilibrium two-qubits systems
• A polaron theory of quantum thermal transistor in nonequilibrium three-level systems
• Three-terminal normal-superconductor junction as thermal transistor
• Quantum vs Classical Thermal Transport at Low Temperatures