Scale Dependence of the Retarded van der Waals Potential

Abstract

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit $\alpha \to 0$ together with the relative distance between the atoms increasing as ${\alpha }^{-\gamma }R$, $\gamma >0$. In particular we determine explicitly the crossover function from the $R^{-6}$ van der Waals potential to the $R^{-7}$ retarded van der Waals potential, which takes place at scale ${\alpha }^{-2}R$.

19 pages

References in corpus (3)

• Van-der-Waals potentials of paramagnetic atoms
• Quantitative estimates on the Hydrogen ground state energy in non-relativistic QED
• Non-analyticity of the groud state energy of the Hamiltonian for Hydrogen atom in non-relativistic QED

Cited by in corpus (1)

• Note on the Retarded van der Waals Potential within the Dipole Approximation