Image method in the calculation of the van der Waals force between an atom and a conducting surface

Abstract

Initially, we make a detailed historical survey of van der Waals forces, collecting the main references on the subject. Then, we review a method recently proposed by Eberlein and Zietal to compute the dispersion van der Waals interaction between a neutral but polarizable atom and a perfectly conducting surface of arbitrary shape. This method has the advantage of relating the quantum problem to a corresponding classical one in electrostatics so that all one needs is to compute an appropriate Green function. We show how the image method of electrostatics can be conveniently used together with the Eberlein and Zietal mehtod (when the problem admits an image solution). We then illustrate this method in a couple of simple but important cases, including the atom-sphere system. Particularly, in our last example, we present an original result, namely, the van der Waals force between an atom and a boss hat made of a grounded conducting material.

Observation of nanoscale opto-mechanical molecular damping as the origin of spectroscopic contrast in photo induced force microscopy

“…While the overall force is attractive, this modification generates an additional distance-dependent repulsive term varying as −( d + 2 a t ) −4 . Similar distance dependences have been predicted in models of the interaction energy of an atomic dipole oscillating close to a conducting sphere 39 . However, as we shall point out in the “Discussion” section, such a distance-dependent loss of signal at tip–sample spacings <9 nm can be due to different loss mechanisms.…”

Semiconductor Physics, Quantum Electronics & Optoelectronics. 2017. V. 20, N 2. P. 185-190. DOI: https://doi.org/10.15407/spqeo20.02.185 London forces in highly oriented pyrolytic graphite

“…5), and the energy depends on its projection on Z axis. Orthogonal to the sample surface electric field E can be found with account of the image method [11], which enables to reduce the quantum mechanical problem to the related classical electrostatic one by putting additional point charges into specific places in bulk media. The electric potential in this configuration can be calculated as being induced by the original dipole and the image dipole (Fig.…”

“…If we have objects of complicated shape and mutual position, an image method allows computing the dispersion van der Waals interaction between a neutral but polarizable atom and a perfectly conducting surface of arbitrary shape. This method has the advantage of relating the quantum problem to a well-known classical one in electrostatics [11]. Casimir force between mirrors in vacuum can now be measured with good accuracy and according to theory, when the effect of imperfect reflection of mirrors is properly taken into account [12].…”

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“…In turn, ÊI = ÊI [ d] represents the field that is induced by the dipole. This can be approximately described in terms of an image dipole below the surface 104,105 . A self-consistent approach also requires that the field acts back onto the atomic dipole.…”