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- W4292201359 abstract "We consider a molecule in the Born-Oppenheimer approximation interacting with a plate of infinite thickness, i.e, a half--space, which is perfectly conducting or dielectric. It is well--known in the physics literature that in this case the atom or molecule is attracted by the plate at sufficiently large distances. This effect is analogous to the well--known van der Waals interaction between neutral atoms or molecules. We prove that the interaction energy $W$ of the system is given by $W(r,v)= -C(v)r^{-3} + mathcal{O}(r^{-4})$, where $r$ is the distance between the molecule and the plate and $v$ indicates their relative orientation. Moreover, $C(v)$ is positive and continuous, thus the atom or molecule is always pulled towards the plate at sufficiently large distances, for all relative orientations $v$. For some specific systems we provide sharper estimates of $W(r,v)$. This asymptotic behavior is well--known in the physics literature, however, we are not aware of any previous rigorous results, even on existence of a ground state of the system. For pedagogical reasons, we often start with the case of a hydrogen atom and then we generalize the arguments to deal with a general molecule." @default.
- W4292201359 created "2022-08-18" @default.
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- W4292201359 date "2020-04-09" @default.
- W4292201359 modified "2023-10-01" @default.
- W4292201359 title "On the van der Waals interaction between a molecule and a half-infinite plate" @default.
- W4292201359 doi "https://doi.org/10.48550/arxiv.2004.04771" @default.
- W4292201359 hasPublicationYear "2020" @default.
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