By William M.R. Simpson
Despite greater than part a century of theoretical paintings, the Casimir impression continues to be no longer as totally understood as a few think. during this treatise, the writer uncovers new puzzles and paradoxes relating this mysterious phenomenon. particularly, he basically demonstrates that the main subtle theories fail while faced with dielectrics during which the refractive index isn't uniform yet steadily changes.
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Additional resources for Surprises in Theoretical Casimir Physics: Quantum Forces in Inhomogeneous Media
10 1 Introduction free field) can be computed as follows. 24) where ρ(k) is a density function. Here, ρ(k) = 2. The volume of free space we are considering is V = L 3 . 12), and then integrating over the azimuth. This quantity is clearly infinite. In order for the subtraction between the two energies to be well˜ both must be submitted to the same defined, renormalising the energy E → E, regularisation: E˜ = lim [E(ξ) − E ∞ (ξ)] . 26) ξ→0 The regularised background energy, pursued in the same spirit as before, takes the form cL ∂ E˜ ∞ =− 2 A 2π ∂ξ ∞ ∞ k dk dk x exp −ξ k x2 + k 2 .
The theory of Casimir-Polder forces has been applied to various phenomena, such as the adsorption of a single atom or molecule to a surface , and fruitfully employed in technological applications, such as the atomic force microscope , whose diagnostic utility is predicated upon the material-dependent variation of the force between a probe particle and the surface being probed. Again, there are different theoretical approaches to this type of problem. 8 This section is especially indebted to the discussion in .
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Surprises in Theoretical Casimir Physics: Quantum Forces in Inhomogeneous Media by William M.R. Simpson