An alternative response to the off-shell quantum fluctuations: a step forward in resolution of the Casimir puzzle

Abstract

The spatially nonlocal response functions are proposed which nearly coincide with the commonly used local response for electromagnetic fields and fluctuations on the mass shell, but differ significantly for the off-shell fluctuating field. It is shown that the fundamental Lifshitz theory using the suggested response functions comes to an agreement with the measurement data for the Casimir force without neglecting the dissipation of free electrons. We demonstrate that reflectances of the on-shell electromagnetic waves calculated using the nonlocal and commonly employed local responses differ only slightly. The Kramers–Kronig relations for nonlocal response functions possessing the first- and second-order poles at zero frequency are derived, i.e., the proposed response satisfies the principle of causality. An application of these results to resolution of the Casimir puzzle, which lies in the fact that the Lifshitz theory is experimentally consistent only with discarded dissipation, is discussed.

No-Slip Boundary Conditions for Electron Hydrodynamics and the Thermal Casimir Pressure

“…Note in particular that the s-polarized modes alone account for nearly the entire difference between the measured Casimir force and the theory based on the local Drude approximation (open dots with error bars [40]). In the no-slip model, their repulsive contribution drops significantly compared to the local Drude model, so that the difference to observations gets smaller [15]. The radiative heat current in Figure 1 (right) is also reduced, but the data are well below the levels observed in Refs.…”

“…In the second case, the modes are called evanescent and they are localised to the vicinity of their sources. (Klimchitskaya and Mostepanenko [15] use the words "on-shell" ("off-shell") for propagating (evanescent) modes, respectively.) There are two transverse polarisations, usually called p (or TM) and s (TE).…”

“…Using the argument principle rather than the Euler-MacLaurin formula to evaluate that difference, brings us back to the real-frequency integral (5). This makes one essential difference with respect to Klimchitskaya and Mostepanenko [15] where a modified surface response was also proposed, but the focus was on the behaviour of the zero'th Matsubara frequency ξ 0 = 0. Further comparison to that paper will be drawn in the Conclusion.…”

“…where the DC conductivity σ 0 can be expressed as a diffusion constant 1/µ 0 σ 0 =λ 2 p /τ that governs the spatio-temporal behaviour of low-frequency magnetic fields [27]. The kine-matic shear viscosity η has also the dimension of a diffusion coefficient [see Equation (15)] η ∼ v 2 F τ = 2 /τ. For the noble metal parameters, we have ∼λ p , and the diffusive behaviour of both types overlaps in space.…”

“…The problem arises, however, that the Casimir force under realistic conditions also contains a temperature-dependent contribution (sometimes this is attributed to "real" rather than "virtual" particles) whose relevant frequencies peak in the infrared (hω ∼ k B T = 25.2 meV at room temperature, for example, Wien's displacement law) [9,10]. Its evaluation requires the knowledge of the infrared conductivity of a metal, but this has been the subject of great discussions-the "Drude vs. plasma" controversy [11][12][13][14][15].…”