Van der Waals interactions: Corrections from radiation in fluids

Abstract

We consider induced van der Waals interactions with corrections due to radiation in fluids consisting of polarizable hard spheres. The fluctuating polarizations are quantized while the positions of particles are treated classically. First the well known result for the induced Casimir free energy for a pair of particles is used to establish the resulting free energy at low density. The Casimir interaction includes the full effect of the quantized radiating electromagnetic field. Then the situation with electrostatic dipole-dipole interactions is considered for general density. For this situation the induced interactions are the van der Waals interactions, and we evaluate numerically the free energy based upon analytic results obtained earlier. These analytic results were obtained by extending methods of classical statistical mechanics to the path integral of quantum mechanics. We have realized that these methods can be extended to time-dependent interactions too. Thus we here also make the extension to the radiating dipole-dipole interaction between pairs of particles to obtain explicit results for more arbitrary fluid densities, and radiation corrections to the induced free energy are found both analytically and numerically.

Uniform quantized electron gas

“…By our computations we find that radiations effects are relatively small compared to the the contribution due to the usual electrostatic interaction alone. This is consistent with the previous study of polarizable hard spheres where the positions of the spheres were treated classically while their oscillating dipole moments were quantized [9]. This is also consistent with previous results for induced Casimir energies that are known to be responsible for the attraction between dielectric media.…”

“…The exchange energy related to radiation can now be found by utilizing the steps for the electrostatic case where the Coulomb interaction is replaced by the radiating interaction from the J 2 term of interaction (9). It is…”

“…Here ψ(k) is again the Coulomb interaction (9). The frequency ω is related to the Matsubara frequency via (sign may depend upon convention)…”

“…The direct interaction between polarizations s 1 and s 2 in vacuum is given by expressions (9) and (10). In a dielectric medium the corresponding interaction should be φε (12,…”

“…In this respect the quantized polarizable fluid of Ref. [5] was extended to include radiating dipolar interactions, and corrections to van der Waals forces or the free energy were obtained for the fluid in bulk [11].…”