|Thermal or Black-Body Radiation|
In General > s.a. radiation [including pressure]; physical
constants [Stefan-Boltzmann constant].
* Idea: Radiation emitted by a perfectly absorbing and emitting body at a fixed temperature T; It describes (maximum) heat transfer from an object in the far field; The calculation of its spectrum was "a loose thread that when tugged (by Planck) would eventually unravel the entire fabric of what had passed for reality."
* Spectrum: It is given by the Planck distribution
E(f, T) df = (2πh/c2) (f 3 / ehf/kT –1) df .
* Stefan-Boltzmann law: For
a macroscopic black body at temperature T,
the total energy emitted per unit surface and unit time is E = σT 4,
with σ the Stefan-Boltzmann constant.
* Wien's law: For a macroscopic black body at temperature T, λmax = (0.0029 m/K) T –1.
* Deviations from the general relations: When the size of the radiating body approaches the typical wavelength of the emitted radiation, the spectrum and radiation rate need to be calculated using a more general and detailed theory rather than following Planck's law, based on fluctuational electrodynamics and the fluctuation–dissipation theorem, and using the objects shape and absorption characteristics.
> Online resources: see Wikipedia's Planck law page.
Phenomenology and Related Effects > s.a. temperature [and Lorentz transformations].
* Energy-level shifts and induced forces: Blackbody radiation around hot objects induces ac Stark shifts of the energy levels of nearby atoms and molecules; These shifts are roughly proportional to the fourth power of the temperature and induce a force decaying with the third power of the distance from the object.
@ General references: Silva e Costa PLA(04) [as seen by moving observer]; Balasanyan & Mkrtchian a0907 [drag on a relativistic moving mirror]; Sonnleitner et al PRL(13) + news pw(13)jul [net attractive force between tiny objects].
@ Radiative heat transfer: Francoeur & Mengüç JQSRT(08) [and fluctuational electrodynamics]; Golyk et al EPL(13)-a1210 [between curved objects, small-distance expansion]; > s.a. Heat Flow.
References > s.a. light and thermodynamic systems [thermal light].
@ General: Planck 06; Agnese et al NCB(99) [simple]; Chang & Guan qp/04 [in a compact space]; Boyer FP(07) [and relativity and discrete charge]; Kramm & Herbert a0801 [using dimensional analysis]; Kramm & Mölders a0901; Smerlak EJP(11) [more consistent derivation]; Marr & Wilkin AJP(12)may [Planck's law in introductory physics]; Ford & O'Connell PRE(13)-a1310 [Lorentz transformation of blackbody radiation].
@ Quantum aspects: Boya et al qp/00 [multiphoton states]; Greffet et al Nat(02)mar, Greffet & Henkel CP(07) [coherent emission]; Johansen JOB(04)qp.
@ History: Boya RACZ(03)phy/04 [Planck 1900]; Varró FNL(06)qp [Einstein's fluctuation formula]; Carvalho Martins a1308-ln [and quantum theory].
@ Coupling to atoms: Fröhlich & Merkli CMP(04)mp [return to equilibrium].
@ Classical derivation: Marshall NC(65); Boyer PRD(84) [from equivalence principle and zero-point radiation].
@ Relativistic: Lee & Cleaver a1507 [inertial and non-inertial reference frames].
@ Quantum-gravity motivated corrections: Kim et al PRD(07)-a0705 [in κ-Minkowski spacetime]; Mania & Maziashvili PLB(11)-a0911 [minimum-length corrections]; Husain et al PRD(13)-a1305 [and evidence for dimensional reduction]; Ramos & Boschi PhyA(14)-a1404 [with compact extra dimensions].
@ Nanoscale objects: Wuttke & Rauschenbeutel PRL(13)-a1209 + news pw(12)sep [and fluctuational electrodynamics]; > s.a. QED phenomenology.
@ Other variations: García-García PRA(08)-a0709 [finite-size corrections]; Moreira & Ribeiro a1512 [massive-photon generalization of the Stefan-Boltzmann law]; > s.a. GUP phenomenology.
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