Non-classical Heat Radiation & Transfer
Breaking the law, at the nanoscale (MITnews, July 29, 2009)
Plank's law can be modified for small objects, and short separations.
"Probing Planck’s Law with Incandescent Light Emission from a Single Carbon Nanotube,"
Y. Fan, S.B. Singer, R. Bergstrom, & B.C. Regan, Phys. Rev. Lett.102, 187402 (2009)
"Probing Planck's Law for an Object Thinner than the Thermal Wavelength,"
C. Wuttke and A. Rauschenbeutel, arXiv:1209.0536 [quant-ph]
"Surface Phonon Polaritons Mediated Energy Transfer between Nanoscale Gaps,"
S. Shen, A. Narayanaswamy, & G. Chen, Nano Lett. 9, 2909 (2009)
Heat transfer between plates diverges at short distances due to evanescent waves (tunneling).
We have generalized the scattering approach to of arbitrary shape and materials,
enabling computation of Casimir forces, as well as radiation and heat transfer.
"Nonequilibrium Electromagnetic Fluctuations: Heat Transfer and Interactions,"
M. Krüger, T. Emig, and M. Kardar, Phys. Rev. Lett. 106, 210404 (2011)
Rytov (1959): 
"Fluctuational QED"
Fluctuating currents in each object are related to its temperature by a fluctuation-dissipation condition:
The EM field due to thermal fluctuations of one object is related to overall Green's function by:
The overall fluctuations with many objects at different temperatures is then given by:
From EM correlations follow the stress tensor and the Poynting vector, hence forces and radiation.
Emission from a single object (Sphere or Cylinder):
Emission is proportional to volume for small objects, crossing over to surface proportionality.
Emission from a cylinder is polarized (also switching as a function of size).
Heat Transfer from a plate to a sphere (and other objects at proximity):
Due to its "divergence" heat transfer is dominated by points of close proximity.
A "Proximity Transfer Approximation (PTA)" with "gradient correction" can by used to compute results for
arbitrary smooth shapes at close proximity.