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.
Highlights
Further with Eq (3.7) one can put RK cK (0) = 3ρ − RK (K 2 + 1)/α for the last term of expression (4.13). With this substitution one will find that the partial differentiation with respect to RK will vanish and will not contribute to ut. This reflects the method used to differentiate the free energy in Ref. 6 where the density distribution ρ({sn}) of polymer configurations is considered constant by differentiation with respect to temperature. (Here RK/η is the corresponding quantity to be kept constant in this respect, according to its definition given by Eq (47) of Ref. 6.) With this we find 1 + αcK (0) K 2 + 1 + αcK (0), (4.18)
SUMMARY We have studied corrections from radiation for a simplified fluid model consisting of hard spheres with fluctuating dipole moments located at their centers
The fluctuating dipole moments are quantized as harmonic oscillators
Summary
One of them is the RPA (random phase approximation) which is in accordance with the van der Waals energy where radiation is absent.[17,18] This has been studied by Lein et al for the uniform electron gas where simulation results with which to compare are available.[19] They point out that the RPA gives too low energy (a situation similar to classical DebyeHuckel theory) This is corrected by including a term in addition to the Coulomb interaction at short range.
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