Scattering approach to near-field radiative heat transfer

TL;DR

This paper develops a quantum scattering framework for near-field radiative heat transfer (NFRHT), linking fluctuational electrodynamics to the Landauer-Büttiker formalism by constructing scattering states for matter excitations and a corresponding scattering matrix. It derives a Landauer-type expression for the average energy current and reveals a non-dissipative reactive contribution that can dominate finite-frequency heat-current noise, emphasizing that measurement conventions matter for these reactive effects. The approach is extended from circuit-like reservoirs to extended bodies, showing a channel-by-channel equivalence to an effective circuit even in planar geometries where surface polaritons mediate transfer; a planar, q-resolved formulation recovers known surface-polariton transfer expressions. Overall, the work provides a unified, microscopic description of NFRHT across diverse systems and clarifies the role of reactive energy storage in heat-current fluctuations, bridging FED, Green’s-function methods, and scattering theory.

Abstract

We formulate the problem of near-field radiative heat transfer as an effective quantum scattering theory for excitations of the matter. Built from the same ingredients as the semiclassical fluctuational electrodynamics, the standard tool to handle this problem, our construction makes manifest its relation to the Landauer-Büttiker scattering framework, which appears only implicitly in the fluctuational electrodynamics. We show how to construct the scattering matrix for the matter excitations and give a general expression for the energy current in terms of this scattering matrix. We show that the energy current has an important non-dissipative contribution that can dominate the finite-frequency noise while being absent in the average current. Our construction provides a unified description of near-field radiative heat transfer in diverse physical systems.

Figures (8)

• Figure 1: Left: Circuit representation of near-field radiative heat transfer (NFRHT) between thermal reservoirs at different temperatures. The reservoirs are modeled as resistors, characterized by their frequency-dependent impedances, $Z_j(\omega)$. Right: An equivalent scattering representation of NFRHT, where transmission lines (TL's) couple through a scattering region. Incoming TL excitations are either reflected back or transmitted to other TL's through the scattering region.
• Figure 2: Representation of a resistor $Z_j(\omega)$ by an extended semi-infinite TL, modeled by a sequence of infinitesimal inductors and capacitors, connected to the rest of the circuit via a linear 4-terminal element ("filter") which transforms a constant impedance of the TL into the given impedance $Z_j(\omega)$.
• Figure 3: Heat-current noise spectrum $W_{11}(\Omega)$ (solid line) and the Büttiker-like contribution $W_{11}^B(\Omega)$ (dashed line), for the circuit mimicking heat transfer via surface polaritons (inset) with $L=44\:\text{pH}$, $C_T=1\:\text{aF}$, $C_c=2.3\:\text{aF}$, $C_+=1.5\:\text{aF}$, $C_-=1.0\:\text{aF}$, $R=44\:\Omega$ at $T_1\to0$, $T_2=300\:\text{K}$.
• Figure 4: Heat-current noise spectrum $W_{11}(\Omega)$ (solid line) and the Büttiker-like contribution $W_{11}^B(\Omega)$ (dashed line) for the circuit shown in the inset. The impedance $Z_1(\omega)$ consists of a parallel $RC$ element galvanically coupled to the second resistor $R$. Here, the $RC$ time is chosen as $T_2 RC/\hbar=50$. Impedance temperature $T_1$ is assumed to be much smaller than the temperature $T_2$ of the second resistor.
• Figure 5: Heat-current noise spectrum $W_{11}(\Omega)$ (solid line) and the Büttiker-like contribution $W_{11}^B(\Omega)$ (dashed line) for the circuit shown in the inset. The impedance $Z_1(\omega)$ consists of a parallel $RLC$ element galvanically coupled to the second resistor $R$. The $RC$ time is chosen as $T_2 RC/\hbar=50$ and the resonance frequency as $T_2 \sqrt{LC} /\hbar=10$. Impedance temperature $T_1$ is assumed to be much smaller than the temperature $T_2$ of the second resistor.