Non-Equilibrium Force & Fluctuational QED
Radiation Pressure is a feature of non-equilibrium steady states with different temperatures
At short scales "near-field effects" due to evanescent waves modify classical "Stefan-Boltzmann" law:
"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)
A generalized approach for computation of Casimir forces, as well as radiation and heat transfer.
"Nonequilibrium Fluctuational QED: Heat Radiation, Heat Transfer and Force,"
G. Bimonte, T. Emig, M. Kardar, and M. Krüger, Annual Review of Condensed Matter Physics 8, 119 (2017)
S.M. 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.
Heat transfer at short distances is dominated by evanescent modes at material dependent resonances.
For a single dominant frequency , the heat flux diverges at small separations as
Consider forces between two spheres at different temperatures:
"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)
Whereas the equilibrium force (attractive) falls off as 1/d6, the non-equilibrium force decays as 1/d2. ( * )
The non-equilibrium force can be attractive and repulsive. ( * )
Unlike in thermal equilibrium, there are points of stable levitation. ( * )
Forces are not equal and opposite, with points of equal force in the same direction! ( * )
Example of non-equilibrium Casimir levitation:
A hot microsphere can levitate on top of a cold plate.
If it cools down (including heat transfer) the sphere will fall down.
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)
"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)
"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)
"Thermalization of Heat radiation of an Individual Object Thinner than the Thermal Wavelength,"
C. Wuttke and A. Rauschenbeutel, Phys. Rev. Lett. 111, 024301 (2013)
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.