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

Movement and Fluctuations of the Vacuum

Quantum fields possess zero-point or vacuum fluctuations which induce mechanical effects, namely generalised Casimir forces, on any scatterer. Symmetries of vacuum therefore raise fundamental questions when confronted with the principle of relativity of motion in vacuum. The specific case of uniformly accelerated motion is particularly interesting, in connection with the much debated question of the appearance of vacuum in accelerated frames. The choice of Rindler representation, commonly used in General Relativity, transforms vacuum fluctuations into thermal fluctuations, raising difficulties of interpretation. In contrast, the conformal representation of uniformly accelerated frames fits the symmetry properties of field propagation and quantum vacuum and thus leads to extend the principle of relativity of motion to uniform accelerations. Mirrors moving in vacuum with a non uniform acceleration are known to radiate. The associated radiation reaction force is directly connected to fluctuating forces felt by motionless mirrors through fluctuation-dissipation relations. Scatterers in vacuum undergo a quantum Brownian motion which describes irreducible quantum fluctuations. Vacuum fluctuations impose ultimate limitations on measurements of position in space-time, and thus challenge the very concept of space-time localisation within a quantum framework. For test masses greater than Planck mass, the ultimate limit in localisation is determined by gravitational vacuum fluctuations. Not only positions in space-time, but also geodesic distances, behave as quantum variables, reflecting the necessary quantum nature of an underlying geometry.Comment: 17 pages, to appear in Reports on Progress in Physic

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

Low temperature expansion in the Lifshitz formula

The low temperature expansion of the free energy in a Casimir effect setup is considered in detail. The starting point is the Lifshitz formula in Matsubara representation and the basic method is its reformulation using the Abel-Plana formula making full use of the analytic properties. This provides a unified description of specific models. We re-derive the known results and, in a number of cases, we are able to go beyond. We also discuss the cases with dissipation. It is an aim of the paper to give a coherent exposition of the topic. The paper includes the derivations and should provide a self contained representation.Comment: Final version, to appear in 'Advances in Mathematical Physics