quantifies the level of power attenuation achieved relative to the multi-mode ballistic case.

Phononic interferometers
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The central question of this paper is whether it is possible to achieve a significant reduction in thermal flux by introducing phononic filters into low-dimensional dielectric bars. In work on TESs, it is common practice to describe the heat flux in the legs by the equation $$P = K \left( T_{C}^{n} - T_{B}^{n} \right),
\label{eq:ThermalFlux}$$ where $K$ is a parameter that determines the overall magnitude of the flux, and $n$ is a parameter that describes the functional dependence on temperature. For truly ballistic transport in a single-mode structure $n=2$, whereas for ballistic transport in a highly multimode structure $n=4$ [@withington2011low]. In general, for diffusive transport in a few-mode structure, $n$ is intermediate between these two values. It follows from Eq. (\[eq:ThermalFlux\]) that the differential thermal conductance is given by $$G = n K T_{C}^{(n-1)}.
\label{eq:ThermalCond}$$ Both $K$ and $n$ change when a phononic filter is introduced, and therefore the flux and thermal conductance can in principle change in different ways. In what follows, we shall measure $K$ and $n$ directly for a variety of filters.

At first sight, it seems as if a suitable 