The hidden negative differential thermal conductance

TL;DR

The study addresses negative differential thermal conductance (NDTC) in a nonequilibrium quantum system of two coupled two-level atoms coupled to distinct reservoirs. It develops a Bloch-Redfield (BR) master equation under Born–Markov with a Drude-cutoff Ohmic bath, linking BR zeroth order to the Lindblad steady state and BR second-order corrections to mean force Gibbs (MFG) features. The key finding is that non-secular BR terms suppress heat currents and generate NDTC, a behavior absent in the Lindblad description, with BR remaining well-behaved in symmetric/weak-coupling limits where Lindblad can be unphysical. This work highlights the necessity of beyond-Lindblad dynamics for accurate quantum thermal transport modeling and informs the design of nanoscale quantum thermal devices such as diodes and transistors.

Abstract

Negative differential thermal conductance (NDTC), a hallmark of nonlinear quantum thermal transport, plays a critical role in the design of quantum thermal devices such as thermal diodes and transistors. The Lindblad dynamics predicts that the heat current through two coupled atoms increases with the increasing temperature difference of two bosonic reservoirs. However, in this paper, we uncover the suppressive effect on the heat current in this nonequilibrium system using the Bloch-Redfield master equations, which indicate the emergence of NDTC. Our findings underscore the crucial role of beyond-Lindblad dynamics in accurately capturing nonlinear features in quantum thermodynamic systems.

Figures (6)

• Figure 1: The schematic illustration of our model, where the dashed line represents weak coupling, and the solid line represents strong coupling. The temperatures of two heat reservoirs are $T_{1}$ and $T_{2}$, the energy separation of two qubits are $\varepsilon _{1}$ and $\varepsilon _{2}$.
• Figure 2: The secondary diagonal elements of the system's steady state or the mean force Gibbs state $\rho_{ij}$ dependent on the temperature of the thermal reservoirs $T_1=T_2=T$. Here we set $\gamma _{1}=0.01,\gamma _{2}=0,\omega _{D}=50,\varepsilon _{1}=5,\varepsilon _{2}=4,g=1$, only the first thermal reservoir interacts with the system. The blue line represents $\rho_{14}$; the red line represents $\rho_{23}$, and the 'o and 'x' labeled points represent the corresponding $\rho_{ij}$ of the mean force Gibbs state. For the inset, $\gamma _{2}=0.01$, while keeping all other parameters unchanged, both thermal reservoirs interact with the system for this case.
• Figure 3: The heat currents ${\mathcal{J}_{1}}$ vs the temperature difference $\Delta T$. Here we set $T_{2}=5,T_{1}=5+\Delta T,\varepsilon_1=5,\varepsilon_2=4,\gamma _{1}=\gamma _{2}=0.01,\omega _{D}=50.$ The blue lines represent the heat current obtained by the Lindblad master equation, and the red lines represent the heat current obtained by the BR master equation. For the solid, dashed, dotted lines, $g=0.75$, $0.5$, $0.25$, respectively.
• Figure 4: The heat currents ${\mathcal{J}_{1}}$ vs the temperature difference $\Delta T$. Here we set $T_{2}=5,T_{1}=5+\Delta T,\varepsilon_1+\varepsilon_2=10,g=0.5,\gamma _{1}=\gamma _{2}=0.01,\omega _{D}=50.$ The blue lines represent the heat current obtained by the Lindblad master equation, and the red lines represent the heat current obtained by the BR master equation. For the solid, dashed, dotted lines, $(\varepsilon_1,\varepsilon_2)=(5.5,4.5)$, $(6,4)$, $(6.5,3.5)$, respectively.
• Figure 5: The heat currents ${\mathcal{J}_{1}}$ versus the temperature difference $\Delta T$. Here we set $T_{2}=5,T_{1}=5+\Delta T,\gamma _{1}=\gamma _{2}=0.01,\omega _{D}=50.$ For the red, blue, and black lines, the parameters are $(\varepsilon_1,\varepsilon_2)=(4,4)$, $(5,5)$, and $(6,6)$ respectively, while for the solid, dashed, and dotted lines, $g=0.2$, $0.1$, and $0.05$ respectively.