Nontrivial retardation effects in dispersion forces: From anomalous distance dependence to novel traps

Abstract

In the study of dispersion forces, nonretarded, retarded and thermal asymptotes with their distinct scaling laws are regarded as cornerstone results governing interactions at different separations. Here, we show that when particles interact in a medium, the influence of retardation is qualitatively different, making it necessary to consider the non-monotonous potential in full. We discuss different regimes for several cases and find an anomalous behaviour of the retarded asymptote. It can change sign, and lead to a trapping potential.

Origin of anomalously stabilizing ice layers on methane gas hydrates near rock surface

“…It is thus worthwhile, in this work, to give some thought to the non-retarded behaviors of multi-layer configurations, including as well three-layer structures. 51 Firstly, we consider the simple case of a three-layer system consisting of nonmagnetic media and arranged as e 1 -e 2 -e 3 , in the non-retarded limit, where the frequency and spatial dependence separates due to the small thickness of the intervening layer d, d { z 1 À1 . In this case, the Casimir-Lifshitz free energy F CL can be expressed in terms of the Hamaker constant 52,53 (A 123 = À12pd 2 F CL ),…”

“…It is thus worthwhile, in this work, to give some thought to the non-retarded behaviors of multi-layer configurations, including as well three-layer structures. 51…”

“…For the case here, a positive sign for A 123 (or A 123;0 ) indicates short range (or long range for A 123;0 ) attraction, while a negative sign indicates repulsion. 51 The different separation regimes for the three-layer interaction are short range non-retarded regime (free energy ∝ d −2 ), retarded regime (free energy ∝ d −3 ), and the long-range thermal regime (free energy ∝ d −2 ). Here, the retardation leads to a reduction of the m > 0 contributions to the Casimir–Lifshitz free energy, leaving long-range results dominated by the m = 0 term (as long as the effect of screening from ions on the m = 0 term at very large separations is negligible).…”

Effective screening of medium-assisted Van der Waals interactions between embedded particles

“…Beyond these extensions, there are some limitations that the model cannot cover: (i) the intermediate regime, where retardation effects start to play a role are not adaptable, because the potential does not factorises into a part depending on the polarizabilities and another part only depending on the dielectric function of the medium [50]; and (ii) in situations, where the interacting atomic systems A and B are so close together that the electronic densities start to overlap and a molecule is formed, the derived model fails due to the coupling dipole-electric field interaction Hamiltonian applied in the whole theory.…”