A microscopic approach to Casimir and Casimir–Polder forces between metallic bodies

Abstract

a b s t r a c tWe consider the Casimir-Polder interaction energy between a metallic nanoparticle and a metallic plate, as well as the Casimir interaction energy between two macroscopic metal plates, in terms of the many-body dispersion interactions between their constituents. Expressions for two-and three-body dispersion interactions between the microscopic parts of a real metal are first obtained, both in the retarded and non-retarded limits. These expressions are then used to evaluate the overall two-and three-body contributions to the macroscopic Casimir-Polder and Casimir force, and to compare them with each other, for the two following geometries: metal nanoparticle/half-space and half-space/half-space, where all the materials are assumed perfect conductors. The above evaluation is obtained by summing up the contributions from the microscopic constituents of the bodies (metal nanoparticles). In the case of nanoparticle/half-space, our results fully agree with those that can be extracted from the corresponding macroscopic results, and explicitly show the non-applicability of the pairwise approximation for the geometry considered. In both cases, we find that, while the overall two-body contribution yields an attractive force, the overall three-body contribution is repulsive. Also, they turn out to be of the same order, consistently with the known non applicability of the pairwise approximation. The issue of the rapidity of convergence of the many-body expansion is also briefly discussed.

Agglomeration compaction promotes corrosion of gold nanoparticles

“…84,85 These forces are caused by fluctuations of electrons and quantum fluctuations whose spectrum is altered by the presence of boundaries. 86–88 It is reasonable to stress that according to theoretical calculations, the light-induced interaction for strongly focused laser beams becomes comparable in strength to the action of Casimir force. 89 When the nonlinear polarizability of nanoparticles is also taken into account, an additional interaction appears, leading to the attractive ponderomotive forces in the system of two nanoparticles.…”

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

“…These results could in principle be extended to generic electrically polarizable bodies. For systems of three or more macroscopic bodies, the non-additivity of dispersion interactions should, however, be taken into account [27,38], and effective Hamiltonians can be very useful in dealing with nonadditive interactions.…”

Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum

“…When comparing the expressions of the minimal coupling Hamiltonian (9) with the multipolar coupling Hamiltonian (19), some important considerations are in order. As already mentioned, in the multipolar scheme, the momentum field conjugate to the vector potential, the transverse displacement field, is different than that in the minimal coupling scheme (i.e., the transverse electric field).…”

“…These forces are non additive, that is, the interaction between three on more atoms is not simply the sum of pairwise interactions; non-additive terms are present, involving coordinates of all atoms [5][6][7]. Nonadditive contributions are usually small for dilute systems, but they can become relevant for dense systems [8,9]. In this paper, we review some properties of two-and three-body dispersion interactions between neutral atoms, both in the nonretarded (van der Waals) and in the retarded (Casimir-Polder) regime, and recent advances in this subject.…”