The heat radiated by objects smaller than or comparable in size to the thermal wavelength can be very different from the classical blackbody radiation as described by the Planck and Stefan-Boltzmann laws. We use methods based on scattering of electromagnetic waves to explore the dependence on size, shape, and material properties. In particular, we explore the radiation from a long cylinder at uniform temperature, discussing in detail the degree of polarization of the emitted radiation. If the radius of the cylinder is much smaller than the thermal wavelength, the radiation is polarized parallel to the cylindrical axis and becomes perpendicular when the radius is comparable to the thermal wavelength. For a cylinder of uniaxial material (a simple model for carbon nanontubes), we find that the influence of uniaxiality on the polarization is most pronounced if the radius is larger than a few micrometers, and quite small for the submicrometer sizes typical for nanotubes.

Near field radiative heat transfer and vacuum friction are just two instances of topics of technological and fundamental interest studied via the formalism of fluctuational electrodynamics. From the perspective of experiment and simulations, it is hard to precisely control and probe such nonequilibrium situations. Fluctuations in equilibrium are easier to measure, and typically can be related to non-equilibrium response functions by Green-Kubo relations. We consider a collection of arbitrary objects in vacuum, perturbed by changing the temperature or velocity of one object. Developing a method for computation of higher order correlation functions in fluctuational electrodynamics, we explicitly compare linear response and equilibrium fluctuations. We obtain a GreenKubo relation for the radiative heat transfer, as well as a closed formula for the vacuum friction in arbitrary geometries in the framework of scattering theory. We comment on the signature of the radiative heat conductivity in equilibrium fluctuations.

We show that roughness or surface modulations change the distance dependence of (power-law) interactions between curved objects at proximity. The modified scaling law is then simply related to the order of the first non-vanishing coefficient of the Taylor expansion of the distribution of separations between the surfaces. The latter can in principle be estimated by scanning measurements, or computed for well characterized modulations, and then used to predict short-distance scaling behavior in disparate experiments. For example, we predict that the radiative heat transfer between a rough sphere and a plate approaches a constant with decreasing separation. Similar saturation is expected for the Casimir force between dielectric or metallic surfaces with appropriate modulations over distinct length scales. 44.40.+a, 68.35.Ct The Proximity Approximation (PA) has long served as a useful guide for estimating interactions between closely spaced objects with curved surfaces. Originally introduced by Derjaguin [1] to compute van der Waals forces between colloidal particles, the PA relates the interaction between curved objects at close separations to the corresponding interaction between two flat surfaces, over an area determined by the local radii of curvature. The PA has been successfully used in experimental studies in a variety of fields, such as quantum Casimir forces [2-4], classical Casimir forces in a fluid near a critical point [5], near field radiative heat transfer [6,7], and interactions among nuclei [8]. Recently it has also been applied to the gravitational force in searches of non-Newtonian gravity [9].In this paper, we utilize PA to investigate scaling of the interaction between two surfaces whose local radii of curvature can be decomposed as the sum of components which vary along the surface on well separated length scales. We note that this situation encompasses the experimentally relevant cases of two large rough objects, such that the correlation length of the roughness is much smaller than the characteristic radius of curvature of the surface, or alternatively the case of a surface with large average radius of curvature modulated by small structures fabricated by the experimenter. We find that at proximity a subtle interplay between roughness/modulation and the global curvature of the surfaces leads to a drastic change in the distance dependence of the interaction, compared to that for perfectly smooth (structureless) surfaces. The modified scaling law is found to depend in a simple way on the order of the first non-vanishing term in the Taylor expansion of the * Present address: 4th Institute for Theoretical Physics, Universität Stuttgart, Germany and Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany height distribution function of the surfaces. The latter is a geometric feature of the surface that can be either computed for well characterized modulations, or experimentally obtained via scanning probes of rough surfaces, and then used to predict the short distance scaling of ...

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-We develop a small distance expansion for the radiative heat transfer between gently curved objects, in terms of the ratio of distance to radius of curvature. A gradient expansion allows us to go beyond the lowest order proximity transfer approximation. The range of validity of such expansion depends on temperature as well as material properties. Generally, the expansion converges faster for the derivative of the transfer than for the transfer itself, which we use by introducing a near-field adjusted plot. For the case of a sphere and a plate, the logarithmic correction to the leading term has a very small prefactor for all materials investigated.More than 40 years ago Van Hove and Polder used Rytov's fluctuational electrodynamics [1] to predict that the radiative heat transfer (HT) between objects separated by a vacuum gap can exceed the blackbody limit [2]. This is due to evanescent electromagnetic fields decaying exponentially into the vacuum. HT due to evanescent waves has also attracted a lot of interest due to its connection with scanning tunnelling microscopy, and scanning thermal microscopy under ultra-high vacuum conditions [3,4]. The enhancement of HT in the near-field regime (generally denoting separations small compared to the thermal wavelength, which is roughly 8 microns at room temperature) has only recently been verified experimentally [5,6]. Theoretically, HT has been considered for a limited number of shapes: Parallel plates [2,3,7,8], a dipole or sphere in front a plate [9][10][11], two dipoles or spheres [9,12,13], and for a cone and a plate [14]. The scattering formalism has been successfully exploited [10,[15][16][17][18] in this context. Although powerful numerical techniques [14,19] exist for arbitrary geometries, analytical computations are limited to planar, cylindrical and spherical cases [18]. Alternatively, the HT between closely spaced curved objects can be computed by use of the proximity transfer approximation (PTA) [10,11,20], which exploits an approach that has been extensively used in the context of fluctuation induced forces [21] (referred to as proximity force approximation): The HT between two parallel plates (per unit area), H pp (S), for separation S is averaged over one of the (projected) curved surfaces. PTA is generally assumed to hold asymptotically for small separations, however no rigorous derivation appears available in the literature.Here we develop a gradient expansion for HT between closely spaced objects, which enables to rigorously justify PTA and to quantify corrections to it in the limit of small separation. This method, which has been proposed for Casimir forces [22][23][24], exploits the mapping of coefficients of a perturbative expansion on one side and a gradient expansion on the other. We carefully explore the limitations and subtleties of this method in the case of HT and propose a near-field adjusted plot that overcomes the possibly slow convergence of the expansion.Consider two non-magnetic objects with dielectric permittivities ǫ 1 (ω) and ...