Non-Equilibrium Force & Fluctuational QED

Radiation Pressure is a feature of non-equilibrium steady states with different temperatures

           

yellow ball At short scales "near-field effects" due to evanescent waves modify classical "Stefan-Boltzmann" law:

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)

A generalized approach for computation of Casimir forces, as well as radiation and heat transfer.

yellow ball  "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"

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.

  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

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.

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 "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)

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)

 

 

red ball  Heat Transfer from a plate to a sphere (and other objects at proximity):

yellow ball Due to its "divergence" heat transfer is dominated by points of close proximity.

yellow ball A "Proximity Transfer Approximation (PTA)" with "gradient correction" can by used to compute results for arbitrary smooth shapes at close proximity.