Spectral overlapD_L(w) vs D_R(w)
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Phonon Junction Explorer
Interactive, layman-friendly view of steady heat flow and conductance trends inspired by the Cuansing-Bautista model. Read article on arXiv
Coupled Harmonic Phonon Reservoirs Model
Reservoir plus junction Hamiltonian
\[
H = H_{\mathrm{L}} + H_{\mathrm{R}} + H_{\mathrm{LR}}
\]
\[
H_{\mathrm{LR}} = \frac{1}{2}k_{\mathrm{LR}}\left(x_1 - x_0\right)^2
\]
Landauer-like heat current
\[
J_{\mathrm{L}} =
\int_{-\infty}^{\infty}\hbar\omega\,T(\omega)\left(f_{\mathrm{L}}-f_{\mathrm{R}}\right)\,d\omega
\]
Differential thermal conductance
\[
K_{\mathrm{L}} =
\int_{-\infty}^{\infty}
\frac{\hbar^2\omega^2}{k_{\mathrm{B}}T_{\mathrm{L}}^2}\,
T(\omega)\,f_{\mathrm{L}}\left(f_{\mathrm{L}}+1\right)\,d\omega
\]
Transmission and steady-state symmetry
\[
T(\omega)=k_{\mathrm{LR}}\,
\mathrm{Im}\!\left[G_{10}^{r}(\omega)\,\Gamma_{00}\,G_{00}^{a}(\omega)\right]
\]
\[
J_{\mathrm{L}} = J_{\mathrm{R}},\qquad K_{\mathrm{L}} = K_{\mathrm{R}}
\]
Live outputs
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Heat current J
Steady current follows Delta T trend.
Conductance kappa
Generally improves with stronger coupling.
Spectral overlap
Larger overlap means better mode matching.
Directional check
Magnitude remains symmetric when reversed.
Heat current responseJ vs Delta T
Bigger temperature gap usually yields stronger steady flow.
Coupling trendkappa vs k_c
Direction symmetryL->R vs R->L
Reversing hot and cold flips direction but preserves magnitude.