QED non-equilibrium

red ball A simple off-equilibrium set-up involves objects at two different temperature, with a resulting heat current.

yellow ball In the QED context, there is radiative heat transfer, and associated radiation pressure.

      

yellow ball Note, that classical "blackbody" formulae break down at scales smaller than the thermal wavelength.

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

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

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

 

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

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

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  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.

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

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

 

Non-Equilibrium Force

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)

yellow ball Whereas the nonequilibrium force 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, but falls if it cools down (due to heat transfer).