Fluctuational Electrodynamics in Atomic and Macroscopic Systems: van der Waals Interactions and Radiative Heat Transfer

We present an approach to describing fluctuational electrodynamic (FED) interactions, particularly van der Waals (vdW) interactions as well as radiative heat transfer (RHT), between material bodies of vastly different length scales, allowing for going between atomistic and continuum treatments of the response of each of these bodies as desired. Any local continuum description of electromagnetic (EM) response is compatible with our approach, while atomistic descriptions in our approach are based on effective electronic and nuclear oscillator degrees of freedom, encapsulating dissipation, short-range electronic correlations, and collective nuclear vibrations (phonons). While our previous works using this approach have focused on presenting novel results, this work focuses on the derivations underlying these methods. First, we show how the distinction between "atomic" and "macroscopic" bodies is ultimately somewhat arbitrary, as formulas for vdW free energies and RHT look very similar regardless of how the distinction is drawn. Next, we demonstrate that the atomistic description of material response in our approach yields EM interaction matrix elements which are expressed in terms of analytical formulas for compact bodies or semianalytical formulas based on Ewald summation for periodic media; we use this to compute vdW interaction free energies as well as RHT powers among small biological molecules in the presence of a metallic plate as well as between parallel graphene sheets in vacuum, showing strong deviations from conventional macroscopic theories due to the confluence of geometry, phonons, and EM retardation effects. Finally, we propose formulas for efficient computation of FED interactions among material bodies in which those that are treated atomistically as well as those treated through continuum methods may have arbitrary shapes, extending previous surface-integral techniques.Comment: 25 pages, 5 figures, 2 appendice

Impact of nuclear vibrations on van der Waals and Casimir interactions at zero and finite temperature

Van der Waals (vdW) and Casimir interactions depend crucially on material properties and geometry, especially at molecular scales, and temperature can produce noticeable relative shifts in interaction characteristics. Despite this, common treatments of these interactions ignore electromagnetic retardation, atomism, or contributions of collective mechanical vibrations (phonons) to the infrared response, which can interplay with temperature in nontrivial ways. We present a theoretical framework for computing electromagnetic interactions among molecular structures, accounting for their geometry, electronic delocalization, short-range interatomic correlations, dissipation, and phonons at atomic scales, along with long-range electromagnetic interactions among themselves or in the vicinity of continuous macroscopic bodies. We find that in carbon allotropes, particularly fullerenes, carbyne wires, and graphene sheets, phonons can couple strongly with long-range electromagnetic fields, especially at mesoscopic scales (nanometers), to create delocalized phonon polaritons that significantly modify the infrared molecular response. These polaritons especially depend on the molecular dimensionality and dissipation, and in turn affect the vdW interaction free energies of these bodies above a macroscopic gold surface, producing nonmonotonic power laws and nontrivial temperature variations at nanometer separations that are within the reach of current Casimir force experiments.Comment: 11 pages, 4 figures (3 single-column, 1 double-column), 2 appendice

A Note On Line Graphs

In this note we define two generalizations of the line graph and obtain some results. Also, we mark some open problems

Mechanical relations between conductive and radiative heat transfer

We present a general nonequilibrium Green's function formalism for modeling heat transfer in systems characterized by linear response that establishes the formal algebraic relationships between phonon and radiative conduction, and reveals how upper bounds for the former can also be applied to the latter. We also propose an extension of this formalism to treat systems susceptible to the interplay of conductive and radiative heat transfer, which becomes relevant in atomic systems and at nanometric and smaller separations where theoretical descriptions which treat each phenomenon separately may be insufficient. We illustrate the need for such coupled descriptions by providing predictions for a low-dimensional system of carbyne wires in which the total heat transfer can differ from the sum of its radiative and conductive contributions. Our framework has ramifications for understanding heat transfer between large bodies that may approach direct contact with each other or that may be coupled by atomic, molecular, or interfacial film junctions.Comment: 16 pages, 2 figures, 1 table, 2 appendice

Non-additivity of van der Waals forces on liquid surfaces

We present an approach for modeling nanoscale wetting and dewetting of liquid surfaces that exploits recently developed, sophisticated techniques for computing van der Waals (vdW) or (more generally) Casimir forces in arbitrary geometries. We solve the variational formulation of the Young--Laplace equation to predict the equilibrium shapes of fluid--vacuum interfaces near solid gratings and show that the non-additivity of vdW interactions can have a significant impact on the shape and wetting properties of the liquid surface, leading to very different surface profiles and wetting transitions compared to predictions based on commonly employed additive approximations, such as Hamaker or Derjaguin approximations.Comment: 5 pages (including abstract, acknowledgments, and references), 3 figure

Sectoral R&D intensity and exchange rate volatility: A panel study on economies of the OECD

A recent literature has pointed at potential negative effects of exchange rate volatility on innovation. In this paper, we propose that there may be a direct effect as well as an indirect effect via export activity. We test these hypotheses for sectoral R&D intensities using OECD panel data for manufacturing and services sectors for 14 OECD economies and the years 1987 - 2003. We find that the direct negative effect of volatility is pronounced in manufacturing sector but is dominated by the indirect effect via the export channel. Services do not face any effects of volatility on R&D intensities. While it is not clear which channel dominates our results confirm that there is a negative volatility affect related to openness on a sectoral level