Beyond Stephan-Boltzmann law

red ball Planck spectrum:                      leads to textbook results:

yellow ball Stefan-Boltzmann law, isotropic radiation emitted by blackbody at temperature T         

yellow ball For two plates at different temperatures               

yellow ball Casimir force (at zero temperature)       

red ball  Radiation Pressure exceeds the Casimir attraction if

yellow ball For distances below this thermal wavelength (around 1.2 microns at room temperature),

"near-field effects" due to evanescent waves lead to non-textbook behavior.

yellow ball "Surface Phonon Polaritons Mediated Energy Transfer between Nanoscale Gaps,"

S. Shen, A. Narayanaswamy, & G. Chen, Nano Lett. 9, 2909 (2009)

 Breaking the law, at the nanoscale (MIT news, July 29, 2009)

 

yellow ball Heat transfer between plates diverges at short distances due to evanescent waves (tunneling).

yellow ball "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)

   

red ballA generalized scattering approach enables computation of Casimir forces, as well as radiation and heat transfer,

in non-equilibrium steady states.

yellow ball "Nonequilibrium Electromagnetic Fluctuations: Heat Transfer and Interactions,"

M. Krüger, T. Emig, and M. Kardar, Phys. Rev. Lett. 106, 210404 (2011)

Rytov (1959):      "Fluctuational QED"

yellow ball Fluctuating currents in each object are related to its temperature by a fluctuation-dissipation condition:

yellow ball The EM field due to thermal fluctuations of one object is related to overall Green's function by:

yellow ball The overall fluctuations with many objects at different temperatures is then given by:

yellow ball From EM correlations follow the stress tensor and the Poynting vector, hence forces and radiation.