原子与赝相对论动能的范德华-伦敦相互作用
Van der Waals-London interaction of atoms with pseudo-relativistic kinetic energy
摘要：
我们考虑一个多原子系统，其中原子核被假定为在固定位置的点电荷。粒子通过库仑势相互作用，电子具有伪相对论性动能。我们证明了范德瓦尔斯-伦敦定律，该定律指出中性原子之间的相互作用能衰减为原子之间距离$|D|$的六次方。我们严格计算了结合能中的所有项，最高可达$|D|^{-9}$阶，误差项为$\mathcal{O}(|D|^{-10})$阶。作为中间步骤，我们证明指数衰减的多粒子薛定谔算子的排列对称性的泡利原理和新的估计的本地化错误。
英文摘要：
We consider a multiatomic system where the nuclei are assumed to be point charges at fixed positions. Particles interact via Coulomb potential and electrons have pseudo-relativistic kinetic energy. We prove the van der Waals-London law, which states that the interaction energy between neutral atoms decays as the sixth power of the distance $|D|$ between the atoms. We rigorously compute all the terms in the binding energy up to the order $|D|^{-9}$ with error term of order $\mathcal{O}(|D|^{-10})$ . As intermediate steps we prove exponential decay of eigenfunctions of multiparticle Schrödinger operators with permutation symmetry imposed by the Pauli principle and new estimates of the localization error.
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