Attractive and Repulsive Casimir–Lifshitz Forces, QED Torques, and Applications to Nanomachines

Dispersion Interaction between Two Hydrogen Atoms in a Static Electric Field

“…The (red) arrows on the atoms indicate the direction of the induced dipole moments. Our results (12),(13), (14) and (15) show that, when E and E are parallel, the change due to the external field is positive (thus yielding a repulsive contribution) in the perpendicular configuration, while it is negative (yielding an attractive contribution) in the parallel configuration. This can be understood with a sharp physical picture in terms of the interaction between the induced atomic dipole moments: in the perpendicular case (panel (a) of Figure 1), the dipole-dipole interaction yields a repulsive force (the interaction energy of one induced dipole in the field generated by the other induced dipole is positive), while in the parallel case (panel (b) of Figure 1) it yields an attractive force (the interaction energy is negative).…”

“…All this indicates a realistic possibility to observe the new effects we have obtained. At shorter distances, our results (12),(13), (14), (15) show that higher field intensities are required in order to make the fieldmediated contribution comparable with the unperturbed one: of the order of 10 6 V/m for r ∼ 100 nm (far zone), and of the order of 10 8 V/m for r ∼ 10 nm (near zone). We just mention that, in the configurations yielding a repulsive field-assisted component of the dispersion force, and at specific distances between the atoms, the external fields can be appropriately calibrated to make the total dispersion interatomic force vanishing (even if this equilibrium interatomic distance turns out to be an unstable point).…”

Derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors

“…This formula shows the nice property of having a completely symmetrical form for the two polarizations but it also leads to a discontinuity in the calculated thermal Casimir pressure when going from a dissipative model (γ = 0) to a non-dissipative one (γ = 0). For thick metallic slabs described by the plasma model, we have found the expression (24) for the Casimir pressure, which is not identical to the one commonly used (5). This follows from the fact that the Matsubara pole for the TE mode at ξ 0 does not contribute for a lossless plasma metal, in spite of a non-vanishing value of r TE k (0, k).…”

“…In the next section, we will go through the same derivation for the plasma model and find an expression looking like (13) but differing from (5). At this point, it is worth emphasizing a few points which have played a role in the derivation of (13).…”

“…The Casimir force [1] is a manifestation of vacuum field fluctuations [2] which is now measured with a good experimental precision in various experiments [3][4][5][6]. However, the comparison of experimental results with theoretical predictions remains a matter of debate [7][8][9].…”