Quantum-thermal fluctuations of electromagnetic waves are the cornerstone of quantum statistics and inherent to phenomena such as thermal radiation and van der Waals forces. Although the principles are found in elementary texts, recent experimental and technological advances make it necessary to come to terms with counterintuitive consequences at short scales\—the so-called near-field regime. We focus on three manifestations: (*a*) The Stefan\–Boltzmann law describes radiation from macroscopic bodies but fails for small objects. (*b*) The heat transfer between two bodies at close proximity is dominated by evanescent waves and can be orders of magnitude larger than the classical (propagating) contribution. (*c*) Casimir forces, dominant at submicron separation, are not sufficiently explored for objects at different temperatures (at least experimentally). We explore these phenomena using fluctuational quantum electrodynamics (QED), introduced by Rytov in the 1950s, combined with scattering formalisms. This enables investigation of different material properties, shapes, separations, and arrangements.

We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals interaction with a gently curved dielectric surface at temperature T, and submicron separations. The molecule is assumed to be in its electronic and vibrational ground state, and the rotational degrees are described by a rigid rotor model. We show that under these conditions retardation effects and surface dispersion can be neglected. The level shifts are found to be independent of T, and given by the quantum state averaged classical electrostatic interaction of the dipole with its image on the surface. We use a derivative expansion for the static Green\&$\#$39;s function to express the shifts in terms of surface curvature. We argue that the curvature induced line splitting is experimentally observable, and not obscured by natural linewidths and thermal broadening.

}, issn = {2469-9926}, doi = {10.1103/PhysRevA.94.022509}, url = {https://link.aps.org/doi/10.1103/PhysRevA.94.022509}, author = {Bimonte, Giuseppe and Emig, Thorsten and Jaffe, R. L. and Kardar, Mehran} } @article {158, title = {Casimir-Polder force between anisotropic nanoparticles and gently curved surfaces}, journal = {Physical Review D}, volume = {92}, year = {2015}, month = {Jul-17-2015}, abstract = {The Casimir--Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO2 and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties.

}, issn = {1550-7998}, doi = {10.1103/PhysRevD.92.025028}, author = {Bimonte, Giuseppe and Emig, Thorsten and Kardar, Mehran} } @article {159, title = {Interplay of curvature and temperature in the Casimir{\textendash}Polder interaction}, journal = {Journal of Physics: Condensed Matter}, volume = {27}, year = {2015}, month = {Jun-03-2015}, pages = {214018}, abstract = {We study the Casimir-Polder interaction at finite temperatures between a polarizable small, anisotropic particle and a non-planar surface using a derivative expansion. We obtain the leading and the next-to-leading curvature corrections to the interaction for low and high temperatures. Explicit results are provided for the retarded limit in the presence of a perfectly conducting surface.

}, issn = {0953-8984}, doi = {10.1088/0953-8984/27/21/214018}, author = {Bimonte, Giuseppe and Emig, Thorsten} } @article {160, title = {Reversing the critical Casimir force by shape deformation}, journal = {Physics Letters B}, volume = {743}, year = {2015}, month = {Apr-09-2015}, pages = {138 - 142}, abstract = {The exact critical Casimir force between periodically deformed boundaries of a 2D semi-infinite strip is obtained for conformally invariant classical systems. Only two parameters (conformal charge and scaling dimension of a boundary changing operator), along withthe solution of an electrostatic problem, determine the Casimir force, rendering the theory practically applicable to any shape and arrangement. The attraction between any two mirror symmetric objects follows directly from our general result. The possibility of purely shape induced reversal of the force, as well as occurrence of stable equilibrium points, is demonstrated for certain conformally invariant models, including the tricritical Ising model.

}, issn = {03702693}, doi = {10.1016/j.physletb.2015.02.038}, author = {Bimonte, Giuseppe and Emig, Thorsten and Kardar, Mehran} } @article {116, title = {Casimir-Polder interaction for gently curved surfaces}, journal = {Physical Review D}, volume = {90}, year = {2014}, month = {Oct-28-2014}, type = {Article}, abstract = {We use a derivative expansion for gently curved surfaces to compute the leading and the next-to-leading curvature corrections to the Casimir-Polder interaction between a polarizable small particle and a nonplanar surface. While our methods apply to any homogeneous and isotropic surface, explicit results are presented here for perfect conductors. We show that the derivative expansion of the Casimir-Polder potential follows from a resummation of its perturbative series, for small in-plane momenta. We consider the retarded, nonretarded and classical high-temperature limits.

}, issn = {1550-7998}, doi = {10.1103/PhysRevD.90.081702}, author = {Bimonte, Giuseppe and Emig, Thorsten and Kardar, Mehran} }