Thermal non-equilibrium

red ball  Radiation Pressure from a hot-plate can in principle counteract Casimir attraction

       cf.   Hieronymus-Bosch,-The-Last-Judgement.-Central-Panel-with-Detail-of-Heaven

yellow ball Around room temperature, this occurs for distances exceeding 7 microns; where the Casimir force is insignificant,

while at short scales "near-field effects" due to evanescent waves modify classical "Stefan-Boltzmann" law:

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.

red ball  Emission from a single object (Sphere or Cylinder):

yellow ball Emission is proportional to volume for small objects, crossing over to surface proportionality.

yellow ball Emission from a cylinder is polarized (also switching as a function of size)

yellow ball "Polarized light emission from individual incandescent carbon nanotubes,"

S. B. Singer, Matthew Mecklenburg, E. R. White, and B. C. Regan, Phys. Rev. B. 83, 233404 (2011)

yellow ball "Thermalization of Heat radiation of an Individual Object Thinner than the Thermal Wavelength,"

C. Wuttke and A. Rauschenbeutel, Phys. Rev. Lett. 111, 024301 (2013)

 

 

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

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

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

 

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

red ball  Consider forces between two spheres at different temperatures:

yellow ball "Non-equilibrium Casimir forces: Spheres and sphere-plate,"

M. Krüger, T. Emig,G. Bimonte and M. Kardar, Europhys. Lett. 95, 21002 (2011) (1 micron Si O2 spheres, force on #2)

yellow ball Whereas the equilibrium force (attractive) falls off as 1/d6, the non-equilibrium force decays as 1/d2. ( * )

yellow ball The non-equilibrium force can be attractive and repulsive.  ( * )

yellow ball Unlike in thermal equilibrium, there are points of stable levitation.  ( * )

yellow ball Forces are not equal and opposite, with points of equal force in the same direction!  ( * )

red ball  Example of non-equilibrium Casimir levitation:

yellow ball A hot microsphere can levitate on top of a cold plate.

yellow ball If it cools down (including heat transfer) the sphere will fall down.